Publication List
Publications in Refereed Journals:
Papers accepted
- (with W. Ao and H. Chan)
Boundary concentrations on segments
for the Lin-Ni-Takagi problem
Annali della Scuola Normale Superiore di Pisa
accepted for publication
-
(with X. Ren)
The spectrum of the torus profile to a geometric variational problem with long range interaction
Physica D: Nonlinear Phenomena
accepted for publication
- (with Hardy Chan)
Travelling wave solutions for bistable fractional Allen-Cahn equations with a pyramidal front.
Journal of Differential Equations
accepted for publication
- (with N. T. Fadai and M.J. Ward)
Delayed reaction-kinetics and the stability of spikes in the Gierer-Meinhardt system
SIAM Journal Applied Math
accepted for publication
- (with A. de la Torre, M. del Pino, Mar del mar Gonzalez)
Delaunay-type singular solutions for the fractional Yamabe problem
Math Annalen
accepted for publication
- (with M. Winter)
Stable spike clusters for the one-dimensional Gierer-Meinhardt system
European Journal of Applied Math
accepted for publication
- (with A. Jevnikar and W. Yang)
Classification of blow-up limits for the Sinh-Gordon equation
Diff. Int. Equations
accepted for publication
- (with A. Jevnikar and W. Yang)
On the topological degree of the mean field equation with two parameters
Indiana Univ. Math. Journal
accepted for publication
- (with S Luo and W. Zou)
On a transcendental equation involving quotients of Gamma functions Proc. AMS
accepted for publication
- (with Kelei Wang)
On Serrin's overdetermined problem and a conjecture of Berestycki, Caffarelli and Nirenberg
Comm. PDE
accepted for publication
- (with H. Kikuchi)
Bifurcation diagram of solutions to elliptic equation with exponential nonlinearity in higher dimensions
Proc. Eding. Math. A.
accepted for publication
- (with Manuel del Pino, M. Musso, C. Roman)
Interior bubbling solutions for the critical Lin-Ni-Takagi problem in dimension 3
Journal d'Analyse Mathematique
accepted for publication
- (with Juan Davila and Manuel del Pino)
Nonlocal $s$-minimal surfaces and Lawson cones
Journal of Differential Geometry
accepted for publication
- (with M. del Pino and O.Agudelo)
Higher dimensional catenoid, Liouville equation and Allen-Cahn equation Liouville's equation
International Math. Research Note (IMRN)
accepted for publication
- (with Y. Sire)
On a fractional Henon equation and applications
Math Research Letters
accepted for publication
- (with M. Fazly)
On finite Morse index solutions of higher order fractional Lane-Emden equation
American Journal of Mathematics
accepted for publication
- (with Juan Davila and L. Dupaigne)
On the fractional Lane-Emden equation
Trans. Amer. Math. Soc.
accepted for publication
- (with Yanyan Li and H. Xu)
Multi-bump solutions of $-\Delta u
=K(x)u^{\frac{n+2}{n-2}}$ on Lattices in ${\mathbb R}^n$
Journal fur die reine und ang. Math. (Crelle's Journal)
accepted for publication
- (with WW Ao and CS Lin)
On non-topological solutions of the $G_2$ Chern-Simons system
Communications Analysis and Geometry
accepted for publication
- (with M. del Pino and O.Agudelo)
Catenoidal layers for the Allen-Cahn equation in bounded domains
Chinese Annals of Mathematics (a special volume for Professor H. Brezis' 70th birthday)
accepted for publication
- (with X.Ren)
A toroidal tube solution of a nonlocal geometric
problem
Interfaces and Free Boundaries accepted for publication.
2016
- (with WW Ao and CS Lin)
On Non-topological Solutions of the $A_2$ and $B_2$
Chern-Simons System (112 pages)
Memoirs of American Mathematical Society
239(2016), no. 1132.
- (with WW Ao, M. Musso and F. Pacard)
Solutions without any symmetry for semilinear elliptic problems
Journal of Functional Analysis
270(2016), no.3, 884-956.
- (with W. Ao and W. Yao)
Uniqueness and nondegeneracy of sign-changing radial solutions of an almost critical problem
Advances in Differential Equations
21(2016), no.11-12, 1049-1084.
- (with Juan Davila and Kelei Wang)
Qualitative Analysis of Rupture Solutions for an MEMS Problem
Ann.Inst. Henri.Poincare NonLinearie
33(2016), no.1, 221-242
- (with Z.Du)
Clustering layers for the Fife-Greenlee problem in $\mathbb{R}^n$
Proc. Royal Soc. Edin. Math Section A
146(2016), no. 1, 107-139.
- (with Z. Du, C. Gui and Y. Sire)
Layered solutions for a fractional inhomogeneous Allen-Cahn equation
NoDEA
23(2016), no.3, 23:29
- (with Changfeng Gui and Yong Liu) On variational characterization of four-end solutions of the Allen-Cahn equation in the plane
Journal of Functional Analysis
271(2016), no. 10, 2673-2700.
- (with ZM Guo and Wen Yang)
On non-radial singular solutions of supercritical bi-harmonic equations
Pacific Journal of Math.
284(2016), no.2, 395-430.
- (with M. Fazly)
On stable solutions of the fractional Henon-Lane-Emden equation
Comm. Contemp. Math.
18(2016), No. 5, 1650005 (24pages)
- (with Meiyue Jiang and Liping Wang)
$2\pi$-periodic self-similar solutions for the anisotropic affine curve
shortening problem II
DCDS-A
36(2016), no.2, 785-803.
- (with CS Lin and L. Zhang)
Local profile of fully bubbling solutions to SU(n+1) Toda Systems
Journal of Europ.Math. Soc. (JEMS)
18(2016), no. 8, 1707-1728.
- (with Bruno Premoselli)
Non-compactness and infinite number of conformal initial data sets in high dimensions
Journal of Functional Analysis
270(2016), no.2, 718-747.
- (with M. Musso)
Sign-changing blowing-up solutions for supercritical Bahri-Corn's problem
CVPDE
55(2016), no.1, 55:1
- (with A. Pistoia and M. Musso) New blow-up phenomena for {\em SU(n+1)} Toda system
JDE
260(2016), no. 7, 6232-6266.
- (with M. Musso and S. Yan)
Infinitely many positive solutions for an nonlinear field equation
with super-critical growth
Proceedings of London Math Society
112(2016), no.1, 1-26.
- (with S. Santra)
Positive solutions of nonlinear Schrodinger equation with peaks on a Clifford torus
Mathematische Nachrichten
289(2016), no. 8-9, 1131-1147.
- (with Santra)
On a singular perturbed problem in an annulus
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
(5)15(2016), 837-857
- (with Kelei Wang)
On the uniqueness of solutions of an nonlocal elliptic system
Math. Annalen
365(2016), no.1-2, 105-153.
- (with Jun Yang)
Traveling vortex helicies for Schr\"odinger Map Equation
Transc. of Amer. Math. Soc.
368(2016), no.4, 2589-2622.
2015
- (with WW Ao and CS Lin)
On Toda system with Cartan matrix $G_2$
Proc. Amer. Math. Soc.
143(2015), no.8, 3525-3536.
- (with M. del Pino and O. Agudelo)
Multiple Catenoidal End Solutions to the Allen-Cahn
Equation in $\R^3$
J. Math. Pures Appl.
103(2015), no.1, 142-218
- (with M. del Pino and F. Pacard)
Serrin's overdetermined problems and constant mean curvature surfaces
Duke Math Journal
164(2015), no.14, 2643-2722.
- (with M. del Pino and Wei Yao)
Intermediate Reduction Methods and Infinitely many positive solutions of nonlinear Schr\"{o}dinger equations with non-symmetric potentials
Cal.Var. PDE
53(2015), no.1-2, 473-523.
- (with M. Fazly and X. Xu)
A point-wise inequality for the fourth order Lane-Emden equation
Analysis & PDE
8(2015), no. 7, 1541-1563.
- (with M. Grossi and F. Gladiali) On a general $SU(3)$ Toda system
CVPDE
54(2015), no.4, 3353-3372.
- (with D. Iron, J. Rumsey, M.J. Ward)
On accurately estimating stability threshold for periodic spot patterns of reaction-diffusion systems in $R^2$
European Journal of Applied Math
26(2015), no.3, 325-353.
- (with M. Kowalczyk and Yong Liu)
Singly periodic solutions of the Allen-Cahn equation and the Toda lattice
Comm. Part. Diff. Eqns.
40(2015), no.2, 329-356.
- (with M. Kowalczyk, Yong Liu and Frank Pacard)
End-to-end construction for the Allen-Cahn equation in the plane
Cal. Var. PDE
52(2015), no.2, 329-356.
- (with CS Lin and L. Zhang)
Classification of blowup limits for $SU(3)$ singular Toda systems
Analysis and PDE
8(2015), no. 4, 807-837.
- (with CS Lin and L. Zhang)
Convergence rate, location and $\partial_z^2$ condition for fully bubbling solutions to $SU(n+1)$ Toda systems
Advances in Mathematics
285(2015), 1189-1224.
- (with M. Musso)
Nondegeneracy of nonradial nodal solutions to Yamabe problem
Comm. Math. Physics
340(2015), no.3, 1049-1107
- (with Xiaofeng Ren) A double bubble assembly as a new phase of
a ternary inhibitory system
Arch Rat Mech Anal
215(2015), no.3, 967-1034.
- (with Kelei Wang)
Analysis of Blow-up Locus and Existence of Weak Solutions for Nonlinear Supercritical Problems
Int. Math. Res. Not. IMRN
2015, no.10, 2634-2670
- (with M. Winter)
Existence and stability of a spike in the central component for a consumer chain model
Journal of Dynamical and Differential Equations
27(2015), no.3-4, 1141-1171.
- (with S. Yan)
Clustered bubbles for An Elliptic problem with critical growth
Nonlinear Analysis:TMA
119(2015), 46-61.
2014
- (with WW Ao)
Infinitely many positive solutions for nonlinear equations with non-symmetric potential
Cal Var. PDE
51(2014), no.3-4, 761-798.
- (with H. Berestycki and M. Winter)
Existence of Symmetric and Asymmetric Spikes for a Crime Hotspot Model
SIAM J. Math. Analysis
46(2014), no.1, 691-719
- (with Juan Davila, Louis Dupaigne and Kelei Wang)
A Monotonicity Formula and a Liouville-type Theorem for a Fourth Order Supercritical Problem
Advances in Mathematics
258(2014), 240-285
- (with Juan Davila and Manuel del Pino)
Concentrating standing waves for the fractional nonlinear Schrodinger equation
J. Diff. Eqns.
256(2014), no.2, 858-892.
- (with Daomin Cao and Z. Liu)
Regularization of point vortices pairs for the Euler equation in dimension two
Archive Rat. Mech. Anal.
212(2014), no.1, 179-217
- (with Y.Guo and B. Li)
Entire nonradial solutions for non-cooperative coupled elliptic system with critical exponents
J. Diff. Eqns.
256(2014), no. 10, 3463-3495
- (with ZM Guo)
Liouville Type Results and Regularity of the Extremal Solutions of Biharmonic equation with negative exponents
DCDS-A 34(2014), no.6, 2561-2580.
- (with ZM Guo)
Rupture solutions of an elliptic equation with a singular nonlinearity
Proc. Roy. Soc. Edin., A 144(2014), no. 5, 905-924.
- (with D. Iron, J. Rumsey and M. Ward )
Logarithmic Expansions and the Stability of Periodic Patterns of Localized Spots for Reaction-Diffusion Systems in $R^2$
Journal of Nonlinear Science
24(2014), no. 5, 857-912.
- (with T. Kolokolnikov and A. Alcolado)
Basic mechanisms driving complex spike dynamics in a chemotaxis model with logistic growth.
SIAM Journal of Applied Mathematics
74(2014), no.5, 1375-1396.
- (with T. Kolokolnikov and M.J. Ward)
The stability of steady-state hotspot patterns for a reaction-diffusion model of urban crime
DCDS-B 19(2014), no.5, 1373-1410.
- (with Xiaofeng Ren)
Double tori solution to an equation of mean curvature and Newtonian potential
Cal Var PDE
49(2014), no.3-4, 987-1018
- (with Xiaofeng Ren) Asymmetric and symmetric double bubbles in
an inhibitory ternary system
SIAM J. Math. Anal.
46(2014), no.4, 2798-2852.
- ( with S. Santra)
Profile of the least energy solution of a singular perturbed Neumann problem with mixed powers
Annali di Matematica Pura ed Applicata
(4) 193(2014), no.1, 39-70.
- (with M. Winter)
Stability of cluster solutions to a tritrophic food chain model
Journal of Mathematical Biology
68(2014), no.1-2, 1-39.
2013
- (with WW Ao and Jing Zeng)
An optimal bound on the number of
interior spike solutions for the Lin-Ni-Takagi problem
Journal of Functional Analysis
265 (2013), no. 7, 1324–1356.
- (with H. Berestycki, TCLin and CY Zhao) On Phase-Separation Model: Asymptotics and Qualitative Properties
Archive Rational Mechanics Analysis 208(2013), no.1, 163-200.
- (with H. Berestycki, S. Terracini and K. Wang)
On Entire Solutions of an Elliptic System Modeling Phase Separations
Advances in Mathematics
243(2013), pp. 102 - 126
- (with M. del Pino and M. Kowalczyk)
Traveling waves with multiple and non-convex fronts for a bistable semilinear parabolic equation
Comm. Pure Appl. Math.
66(2013), no.4, 481-547.
- (with M. del Pino and M. Kowalczyk)
Entire Solutions of the Allen-Cahn Equation and Complete Embedded Minimal Surfaces of Finite Total Curvature
Journal of Differential Geometry 83(2013), no.1, 67-131.
- (with Yanheng Ding and T. Xu)
Existence and concentration of semi-classical solutions for an
nonlinear Maxwell-Dirac system
Journal of Mathematical Physics
54(2013), no.6, 061505, 33pp.
- (with Yuxia Guo and B. Li)
Large energy entire solutions for the Yamabe type problem of polyharmonic operator
J. Diff. Eqns. 254(2013), no.1, 199-228
- (with E. Hebey)
Schrodinger-Poisson system in the 3-sphere
Cal Var PDE 47(2013), no.1-2, 25-54.
- (with Fouad Hadj Selem and Hiroaki Kikuchi)
Existence and uniqueness of singular solution
to stationary Schr\"{o}dinger equation with supercritical nonlinearity
DCDS-A 33 (2013), no. 10, 4613–4626.
- (with T. Kolokolnikov and W. Yang)
On large ring solutions for Gierer-Meinhardt system in $R^3$
Journal of Differential Equations
255(2013), no.7, 1408-1436.
- (with TC Lin and Jun Yang)
Vortex rings for the Gross-Pitaevskii equation in $\R^3$
J. Math. Pures Appl. (9) 100(2013), no.1, 69-112.
- (with L.Ma)
Stability and multiple solutions to
Einstein-scalar field Lichnerowicz equation on manifolds
J. Math. Pures App. (9)99(2013), no.2, 174-186.
- (with Frank Pacard)
Stable solutions of the Allen-Cahn equation in dimension $8$ and minimal cones
Journal of Functional Analysis 264(2013), no.5, 1131-1167.
- (with Xiaofeng Ren)
A double bubble in a ternary system with long range interaction.
Archive Rational Mech. Analysis
208(2013), no.1, 201-253.
- (with S. Santra)
New entire positive solution for the nonlinear Schr\"{o}dinger equation: Coexistence of fronts and bumps
American Journal of Mathematics
135(2013), no.2, 443-491.
- (with F. Ting)
Multi-vortex non-radial solutions to the magnetic Ginzburg-Landau equations
Comm. Math. Phys. Volume 317, Issue 1 (2013), Page 69-97
- (with L. Wang)
Infinite Multiplicity for an Inhomogeneous Supercritical Problem in Entire Space
Comm. Pure Appl. Anal.
12(2013), No. 3, 1243-1257.
- (with Kelei Wang)
On solutions with polynomial growth to an autonomous nonlinear elliptic problem
Advance Nonlinear Studies 13(2013), no.4, 921-932.
- (with Xingwang Xu and Wen Yang)
On the classification of stable solution to biharmonic problems in large dimensions
Pacific Journal of Mathematics
263(2013), no.2, 495-512.
- (with S. Yan )
Infinitely many non-radial solutions for the H\'enon equation with critical growth
Revista Matematica Iberoamericana 29(2013), no.3, 997-1020
- (with Dong Ye)
Liouville Theorems for finite Morse index solutions of Biharmonic problem
Mathematische Annalen 356(2013), no.4, 1599-1612.
- (with C.Zhao)
Non-compactness of the Prescribing $Q-$curvature problem in large dimensions
Cal. Var. PDE 46(2013), No.1, 123-164
2012
- (with A. Aftalion and P. Mason)
Vortex-peak interaction and lattice shape in rotating two-component Bose-Einstein condensates.
Physical Review A 85(2012), no.3, 033614.
- (with Wenyi Chen and S. Yan)
Infinitely many solutions for the Schr\"odinger equations in
$\R^N$ with critical growth
Journal of Differential Equations
252(2012), no.3, 2425-2447.
- (with J. Davila)
Point ruptures for a MEMS equation with fringing field
Comm. Part. Diff. Eqns. 37(2012), 1462-1493.
- (with EN Dancer and ZM Guo)
Non-radial singular solutions of Lane-Emden
equation in $R^N$
Indiana Univ. Math. Journal 61(2012), no.5, 1971-1996.
- (with Manuel del Pino and Mike Kowalczyk)
On De Giorgi's conjecture and beyond
Proceedings of National Acad. of Sciences (PNAS) 109(2012), vol. 18, 6845-6850.
- (with E. Hebey)
Resonant states for the static Klein-Gordon-Maxwell-Proca system
Math Research Letters 19(2012), no.4, 953-967.
- (with Chang-Shou Lin and Dong Ye)
Classification and nondegeneracy of $SU(n+1)$ Toda system with singular sources Inventiones Mathematicae 190(2012), no.1, 169-207.
- (with Chang-Shou Lin and Chunyi Zhao)
Sharp estimates for fully bubbling solutions of a SU(3) Toda system
Geom. Funct. Anal. 22(2012), no.6, 1591-1635.
- (with CSLin and CY Zhao)
Asymptotic behavior of $SU(3)$ Toda system in a bounded domain
Manuscripta Math. 137(2012), no.1-2, 1-18.
- (with Monica Musso)
Nonradial solutions to critical elliptic equations of Caffarelli-Kohn-Nirenberg type
International Mathematics Research Notices.
18(2012), 4120-4162.
- (with Frank Pacard and M. Musso) Finite-energy sign-changing
solutions with dihedral symmetry for the stationary non linear
Schr\"{o}dinger equation Journal of European
Mathematical Society 14(2012), no.6, 1923-1953.
- (with A. Pakylak and F. Ting)
Multi-vortex solutions to Ginzburg-Landau equations with external potential
Archive Rational Mech. Analysis
204(2012), no.1, 314-354.
- (with M. Winter)
Flow-Distributed Spikes for Schnakenberg Kinetics
Journal of Mathematical Biology 64(2012), no.1-2, 211-254.
- (with Jun Yang)
Vortex rings pinning for the Gross-Pitaevskii equation in three dimensional space
SIAM Journal of Mathematical Analysis 44(2012), no.6, 3991-4047.
- (with W. Yao)
Uniqueness of positive solutions to some coupled nonlinear Schr\"{o}dinger equations
CPAA
11(2012), no.3, 1003-1011
2011
- (with Weiwei Ao and M. Musso)
On Spikes Concentrating on Line-Segments to a
Semilinear Neumann Problem
Journal of Differential Equations
251(2011), no.4-5, 881-901.
- (with Weiwei Ao and M. Musso)
Triple Junction Solutions for a Singularly Perturbed Neumann Problem
SIAM Journal of Mathematical Analysis
43(2011), no.6, 2519-2541.
- (with D. Cao and I. Chern)
On ground states of spinor Bose-Einstein condensates
NoDEA 18(2011), no.4, 427-445.
- (with E.Dancer and S. Santra)
Least energy nodal solution of a singular perturbed problem with jumping
nonlinearity Annali della Scuola Normale Superiore di Pisa, Classe di Scienze. (5) 10(2011), no.1, 19-36.
- (with O. Druet and F. Robert)
The Lin-Ni's problem for mean convex domains
Memoirs of American Mathematical Society
November 30, 2011
- (with Manuel del Pino)
Solutions to the Allen-Cahn Equation and Minimal Surfaces
Milan Journal of Mathematics
79(2011), 39-65.
- (with M. del Pino and M. Kowalczyk)
On De Giorgi Conjecture in Dimensions $N \geq 9$ (final version)
Annals of Mathematics 174 (2011), no.3, 1485-1569.
- (with Yuxin Ge and Feng Zhou)
A critical elliptic problem for polyharmonic operators
J. Funct. Analysis 260(2011), no.8, 2247-2282.
- (with ZM Guo)
Global solution branch and Morse index estimates of a semilinear
elliptic equation with super-critical exponent
Trans. American Math. Soc.
363(2011), no.9, 4777-4799
- (with Z. Guo, Z. Liu F. Zhou)
Bifurcations of some elliptic problems with a singular
nonlinearity via Morse index
CPAA 10(2011), no.2, 507-525.
- (with Meiyue Jiang and LP Wang)
$2\pi$-periodic self-similar solutions for the anisotropic affine curve
shortening problem
Cal. Var. PDE 41(2011), no.3-4, 535-565.
- (with Theodore Kolokolnikov)
Stability of spiky solutions in a competition model with cross-diffusion
SIAM Journal of Applied Mathematics
71(2011), no.4, 1428-1457.
- (with CS Lin and LP Wang)
Topological Degree For Solutions of A Fourth Order Mean Field Equation
Math. Zeit
268(2011), 675-705.
- (with S. Santra)
Asymptotic behavior of solutions of a biharmonic Dirichlet problem with
large exponents
Journal d'Analyse Math. 115(2011), 1-31.
- (with L. Wang and S. Yan)
On Lin-Ni's Conjecture in Convex Domains
Proc. London Math. Soc. 102(2011), 1099-1126.
- (with L. Wang and J. Yang)
On Ambrosetti-Malchiodi-Ni Conjecture for General Hypersurfaces
Communications in Part. Diff. Eqns.
36(2011), vol. 12, 2117-2161
- (with L. Wei and F. Zhou)
Mixed interior and boundary nodal bubbling solutions for a sinh-Poisson equation Pacific Journal of Mathematics 250(2011), no.1, 225-256.
- (with W. Yao)
Asymptotic axisymmetry of the
subsonic traveling waves to the Gross-Pitaevskii equation
Comm. Contemp. Math.
13(2011), no.6, 1095-1104.
- (with S. Yan)
Infinitely many positive solutions for an elliptic problem with critical or super-critical growth
J. Math Pures Appl. (9) 96(2011), no.4, 307-333.
- (with CY Zhao and F. Zhou)
On nondegeneracy of solutions of $SU(3)$ Toda system
CRAS 349(2011), no.3-4, 185-190.
- (with EN Dancer and S. Santra)
Asymptotic behavior of the least energy solution of a problem with competing powers
Journal of Functional Analysis
261(2011), 675-705.
2010
- (with H. Berestycki)
On Least Energy Solutions to A Semilinear Elliptic Equation in A Strip
DCDS-A
28(2010), no.3, 1083-1099
- (with EN Dancer and T. Weth)
A priori bounds versus multiple existence of positive solutions for a nonlinear Schrodinger system
AIHP
27 (2010), pp. 953-969
- (with Manuel del Pino and M. Kowalczyk)
The Jacobi-Toda system and foliated interfaces
DCDS-A
28(2010), no.3, 975-1006.
- (with M. del Pino, M. Kowalczyk and F. Pacard)
The Toda system and multiple-end solutions of autonomous planar elliptic problems
Advances in Mathematics
224(2010), no.4, 1462-1516.
- (with M. del Pino, M. Kowalczyk and F. Pacard)
Multiple-end solutions to the Allen-Cahn equations in $R^2$
Journal of Functional Analaysis
258(2010), no.2, 458-503.
- (with Manuel del Pino, M. Kowalczyk and Jun Yang)
Interface foliation near minimal submanifolds in Riemannian
manifolds with positive Ricci curvature
Geom. Funct. Anal. 20(2010), no.4, 918-957.
- (with Qiang Du and C. Zhao)
Vortex Solutions of the High-$\kappa$ High-field Ginzburg-Landau
Model with an Applied Current
SIAM J. Math. Anal. 42(2010), no.6, 2368-2401.
- (with ZM Guo)
Qualitative properties of entire radial solutions for a biharmonic equation
with supcritical nonlinearity
Proc. American Math. Soc.
138(2010), no.11, 3957-3964.
- (with FH Lin)
Traveling Wave Solutions of Schr\"odinger Map Equation
Comm. Pure Appl. Math. 63(2010), no.12, 1585-1621.
- (with TC Lin and Xiaojin Chen) Blow up and solitary waves with
ring profiles for two-component nonlinear Schrodinger equations
Phys. D: Nonlinear Phenomena
239(2010), no.10, 613-626.
- (with T-C Lin and W. Yao)
Orbital stability of bound states of nonlinear
Schr\"{o}dinger equations with linear and nonlinear lattices
J. Diff. Eqns. 249(2010), no.9, 2111-2146.
- (with H. Tse and M. Winter)
The Gierer-Meinhardt System on a Compact
Two-Dimensional Riemannian Manifold: Interaction of Gaussian Curvature and
Green's Function
J. Math. Pures Appl.
94(2010), no.4, 366-397.
- (with Liping Wang and Shusen Yan)
A Neumann Problem with Critical Exponent in Non-convex Domains and
Lin-Ni's Conjecture
Transcation of Amer. Math. Soc.
362(2010), no.9, 4581-4615.
- (with M. Winter)
Stability of Spiky Solutions
in a Reaction-Diffusion System with Four Morphogens
on the Real Line
SIAM J. Math. Anal. 42(2010), no.6, 2818-2841.
- (with S. Yan)
On an elliptic problem with critical growth
and a stronger Lazer-McKenna conjecture
Ann. Scuola. Norm. Pisa
(5)9(2010), no.2, 423-457.
- (with S. Yan)
Infinitely many positive solutions for the nonlinear Schr\"odinger equations
in $ R^N$ Cal.Var. PDE
37(2010), 423-439.
- (with Shusen Yan)
Infinitely many solutions for the prescribed scalar curvature
problem on $\Sn^N$
Journal Functional Analysis
258(2010), 3048-3081.
- (with Jun Yang)
Toda system and cluster phase transition layers in an inhomogeneous phase
transition model
Asymptotic Analysis
69(2010), no.3-4, 175-218.
- (with Dong Ye)
On MEMS equations with fringing fields
Proc. American Math. Soc.
138(2010), no.5, 1693-1699.
2009
- (with E.N. Dancer)
Spike Solutions in coupled nonlinear Schr\"odinger equations with
Attractive Interaction
Transc. American Math. Soc. 361(2009), no.3, 1189-1208.
- (with P. Esposito)
Non-simple Blow-up Solutions for the Neumann two-dimensional $\sinh-$Gordon equation
Cal Var. PDE 34(2009), no.3, 341-375.
- (with YX Guo)
Supercritical biharmonic elliptic problems in domains with small holes
Math. Nach. 282(2009), no.12, 1724-1739.
- (with D. Iron, T. Kolokolonikov, J. Rumsey )
Stability of curved interfaces in the perturbed two-dimensional Allen-Cahn system
SIAM Journal of Applied Math.
69(2009), no.5, 1228-1243.
- (with Theodore Kolokolnikov and M. Ward)
Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain
Journal of Nonlinear Science 19(2009), no.1, 1-56.
- (with T. Kolokolnikov and M. Winter)
Existence and Stability Analysis of
Spiky Solutions for the Gierer-Meinhardt System with Large Reaction Rates
Physica D: Nonlinear Phenomena
238(2009), no.16, 1695-1710.
- (with Fanghua Lin and Taichia Lin)
Skymions in Gross-Pitaevskii Functionals
Acta Mathematica Scientia
2009, 29B(3): 751-776. Special Volume dedicated to Prof. Wu Wenjun's 90th birthday.
- (with PK Maini and M. Winter)
Stability of Spikes in the Shadow Gierer-Meinhardt system with
Robin Boundary Conditions
Chaos (special issue on pattern formations in reaction-diffusion systems)
17(2009),037106, 16pp. .
- (with X.Ren)
On a phase field problem driven by interface tension and interface curvature
Eur.J. Appl.Math.
20(2009), no.6, 531-556.
- (with X. Ren)
Oval shaped droplet solutions in the saturation process of some pattern formation problems
SIAM Journal of Applied Mathematics
70(2009), no.4, 1120-1138.
- (with S.Santra)
Homoclinic solutions for fourth order travelling wave equations
SIAM J. Math. Anal.
41(2009), no.5, 2038-2056.
- (with M. Winter)
Spikes for the Gierer-Meinhardt system with discontinuous diffusion coefficients
Journal of Nonlinear Science
19(2009), no.3, 301-339.
- (with M. Winter)
Strongly Interacting Bumps for the Schrodinger-Newton Equations
Journal of Mathematical Physics
50(2009), no.1, 012905.
- (with M. Winter)
On the Gierer-Meinhardt system with precursors
DCDS-A, special issue for Prof. Mimura's 65th Birthday
25(2009), no.1, 363-398.
- (with Xingwang Xu)
Prescribing $Q-$curvature problem on $S^n$
Journal of Functional Analaysis
257(2009), no.7, 1995-2023.
- (with J. Yang)
Solutions with transition layer and spike in an inhomogeneous phase transition model
Journal of Differential Equations
246(2009), no.9, 3642-3667.
2008
- (with C. Bandle)
Multiple Clustered Layer Solutions for Semilinear Elliptic Problems on $S^n$
Comm. Partial Diff. Equations 33(2008), no.4-6, 613-635.
- (with Juan D\'avila, Manuel del Pino and Monica Musso)
Fast and slow decay solutions for supercritical elliptic
problems in exterior domains
Calculus of Variations and PDE 32(2008), no.4, 765-786.
- (with Manuel del Pino and Mike Kowalczyk )
The Toda system and clustering interfaces in the Allen-Cahn
equation
Archive Rational Mechanical Analysis 190(2008), no.1, 141-187.
- (with M. del Pino and M. Kowalczyk)
On De Giorgi Conjecture in Large Dimensions
C. R. A. S.
346(2008), no.23-24, 1261-1266.
- (with Y. Ding)
Stationary states of nonlinear Dirac equations with general
potentials
Reviews in Mathemmatical Physics 20(2008), no.8, 1007-1032.
- (with ZM Guo)
Asymptotic Behavior of touch-down solutions and global bifurcations
for an elliptic problem with a singular nonlinearity
Comm. Pure Appl. Anal.
7(2008), no.4, 765-786.
- (with ZM Guo)
Infinitely many turning points for an elliptic problem with a
singular nonlinearity
Journal of London Mathematical Society, 78(2008), no.1, 21-35.
- (with Z.M. Guo)
Entire solutions and global bifurcations for a biharmonic equation with singular nonlinearity in $\mathbb R^3$
Adv. Diff. Eqns. 13(2008), no.7-8, 743-780.
- (with ZM Guo)
On a fourth order elliptic problem with negative exponent
SIAM J. Math. Anal.
40(2008/09), no.5, 2034-2054.
- (with ZM Guo)
On solutions with point ruptures for a semilinear Elliptic
problem with singularity
Methods of Analysis and Applications, special issue on MEMS 15(2008), no.3, 377-390.
- (with YX Guo)
Nonexistence of positive finite Morse index solutions to an elliptic problem with singular nonlinearity
Methods of Analysis and Applications, special issue on MEMS 15(2008), no.3, 377-390.
- (with Theodore Kolokolnikov)
Positive Clustered Layered Solutions For the Gierer-Meinhardt System
Journal of Differential Equations 245(2008), no.4, 964-993.
- (with TC Lin)
Orbital stability of bound states of semi-classical nonlinear
Schr\"{o}dinger equations with critical nonlinearity
SIAM J. Mathematical Analysis 40(2008), no.1, 365-381.
- (with Li Ma)
Properties of positive solutions to an Elliptic Equation with
negative exponent
Journal of Functional Analysis 254(2008), no.4, 1058-1087.
- (with F.Mahmoudi and A. Malchiodi)
Transition Layer for the Heterogeneous Allen-Cahn Equation
Ann. Non linearie, Annoles de l'Institut H. Poincare, 25(2008), no.3, 609-631.
- (with X. Ren)
The critical mass constraint in the Cahn-Hilliard equation
Interfaces and Free Boundary Problems 10(2008), no.3, 301-338.
- (with X. Ren)
Spherical solutions to a free boundary problem from diblock copolymer morphology
SIAM Journal of Mathematical Analysis 39(2008), no.5, 1497-1535.
- (with F. Robert)
Asymptotic behavior of a fourth order equation with Dirichlet boundary condition
Indiana Univ. Math. J. 57(2008), no.5, 2039-2060.
- (with Wang Hung Tse and M. Winter)
Spikes for the Gierer-Meinhardt System with Many Segments of
Different Diffusivities
Bulletin of Academia Sinica (New Series), Special volume in celebration of Prof. M. Mimura's 65th birthday
3(2008), no.4, 525-566.
- (with Liping Wang)
Solutions with Interior Bubble and Boundary Layer for an Elliptic
Problem
DCDS-A (special volume in celebration of Dancer's sixtieth birthday) 21(2008), no.1, 333-351.
- (with Tobias Weth )
Radial solutions and phase separation in a system of two coupled Schr\"odinger equations,
Archive Rational Mechanical Analysis 190(2008), no.1, 83-106.
- (with T. Weth)
Asymptotic behavior of solutions of planar elliptic
systems with strong competition
Nonlinearity 21(2008), no.2, 305-317.
- (with M. Winter)
Stationary Multiple Spots for Reaction-Diffusion Systems
Journal of Mathematical Biology 57(2008), no.1, 53-89.
- (with M. Winter)
Mutually Exclusive Spiky Pattern and Segmentation Modeled by the
Five-Component Meinhardt-Gierer System
SIAM J. Appl. Math. 69(2008), no.2, 419-452.
- (with Jun Yang)
Toda system and interior clustering line concentration for a singularly perturbed Neumann problem in two dimensional domain
DCDS-A 22(2008), no.3, 465-508.
- (with Dong Ye)
Nonradial solutions for a conformally invariant fourth order equation in $R^4$
Cal. Var. PDE 32(2008), no.3, 373-386.
- (with F. Zhou and Dong Ye)
Analysis of boundary bubbling solutions for an anisotropic Emden
-Fowler equation, Ann. Non linearie, Annoles de l'Institut H. Poincare, 25(2008), no.3, 425-447.
2007
- (with C. Bandle)
Nonradial Clustered Spike Solutions for Semilinear Elliptic Problems
on $S^n$ J' Analyse Math. 102(2007), 181-208.
- (with T. Bartsch and Zhi-qiang Wang)
Bound states for a coupled nonlinear Schrodinger system
JFPTA 2(2007), no.2, 353-367.
- (with E.Dancer)
Sign-changing solutions for supercritical elliptic problems in domains with small holes
Manuscripta Mathematica 123(2007), no.4, 493-511.
- (with D'Aprile) Clustered Solutions Around Harmonic Centers to a Coupled
Elliptic System . Ann. Non linearie, Annoles de l'Institut H. Poincare, 24(2007), no.4, 605-628
- (with Juan D\'avila, Manuel del Pino and M. Musso)
Standing waves for supercritical nonlinear Schr\"odinger
equations
. Journal of Differential Equations 236(2007), no.1, 164-198.
- (with M. del Pino and M. Kowalczyk)
Concentration on curves for
nonlinear Schr\"odinger equations
Communications on Pure and Applied Mathematics 60 (2007), no. 1, 113-146.
- (with M. del Pino) Supercritical elliptic problems in domains with small holes . Ann. Non linearie, Annoles de l'Institut H. Poincare, 24(2007), no.4, 507-520.
- (with YH Ding)
Semiclassical states for nonlinear Schrodinger equations with sign-changing potentials Journal of Functional Analysis 251(2007), no.2, 546-572.
- (with Th. Kolokolnikov and Michael Ward )
Self-replication of mesa patterns in reaction-diffusion systems,
Physica D: Nonlinear Phenomena 236(2007), no.2, 104-122.
-
(with Z. Guo)
Symmetry of Nonnegative Solutions of a Semilinear
Elliptic Equation with Singular Nonlinearity
. Proc. Royal. Soc. Edinburgh.
Section A. (Mathematics) 137(2007), no.5, 963-994.
- (with Guo ZM)
On the Cauchy problem for a reaction-diffusion equation
with a singular nonlinearity
J. Diff. Eqns. 240(2007), 181-208.
- (with F.-H. Lin and W.-M. Ni) On the Number of Interior Peak Solutions for A Singularly Perturbed Neumann Problem Communications on Pure and Applied Mathematics 60 (2007), no. 2, 252-281.
- (with C.-S. Lin) Uniqueness of multiple-spike solutions via the Method of Moving Planes Pure and Applied Mathematics, A Quarterly Journal (special volume in honour of L. Simon's 60th birthday), 3(2007), no.2, part 2, 689-735.
- (with CS Lin)
Sharp Estimates For Bubbling Solutions of A Fourth Order Mean Field Equation
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, (5)6(2007), no.4, 599-630.
- (with CS Lin and L. Wang)
Bubble Accumulations In An Elliptic Neumann Problem With Critical Sobolev Exponent
. Cal. Var. PDE 30(2007),no.2, 153-182.
- (with TCLin)
Half-Skyrmions and Spike-Vortex Solutions of Two-component Nonlinear Schr\"{o}dinger Systems
. Journal of Mathematical Physics 48(2007), no.5, 053518.
- (with A. Malchiodi)
Boundary Interface for the Allen-Cahn Equation
Journal of Fixed Point Theory and Applications (JFPTA) 1(2007), no.2, 305-336.
- (with A. Malchiodi and W.-M. Ni) Boundary Clustered Interfaces for Allen Cahn Equation
. Pacific Journal of Mathematics , 229(2007), no.2, 447-468.
- (with J. Norbury and M. Winter)
Stability of patterns with arbitrary period
for a Ginzburg-Landau equation with a mean
field . European Journal of Applied Mathematics 18(2007), no.2, 129-151.
- (with Xiaofeng Ren)
Single droplet pattern in the cylindrical phase of
diblock copolymer morphology
Journal of Nonlinear Science 17(2007), no.5, 471-503
- (with X. Ren)
Many droplet pattern in the cylindrical phase of
diblock copolymer morphology
Reviews in Mathematical Physics 19(2007), no.8, 879-921.
- (with M. Winter)
Symmetric and asymmetric clusters in an elliptic system. NoDEA, 14(2007), no.5-6, 787-823.
- (with M. Winter)
Existence, Classification and Stability Analysis of Multiple-peaked Solutions
for the Gierer-Meinhardt System in $R^1$
Methods Appl. Anal. 14(2007), no.2, 119-163.
- (with Tobias Weth )
Nonradial Symmetric Bound States for a System of Coupled Schr\"odinger
Equations
Rendiconti Lincei:Matematica e Applicazioni 18(2007), no.3, 279-293.
- (with S. Yan) Arbitrary many boundary peak solutions for An Elliptic Neumann problem
with critical growth
J. Math. Pures Appl. (9)88(2007), no.4, 350-378.
- (with S. Yan)
Lazer-Mckenna conjecture: the critical case . Journal of Functional Analysis 244(2007), 639-667.
- (with S. Yan)
New Solutions For Nonlinear Schr\"odinger Equations with critical
nonlinearity
. Journal of Differential Equations 237(2007), no.2, 446-472.
- (with Jun Yang)
Concentration on Lines for a Singularly Perturbed Neumann Problem
in Two-Dimensional Domains , Indiana Univ. Math. Journal, 56(2007), no.6, 3025-3073.
- (with D. Ye and F. Zhou)
Bubbling Solutions for an Anisotropic Emden-Fowler Equation
Cal. Var. and Part. Diff. Eqns. 28(2007), 217-247.
2006
- (with T. D'Aprile) Standing waves in the Maxwell-Schrodinger qquation and an optimal configuration problem. Cal. Var. and PDE, 25(2006), 105-137.
- (with D'Aprile)
Layered solutions for a semilinear elliptic system in a ball
J. Diff. Eqns. 226(2006), 269-294.
- (with T. D'Aprile) Boundary Concentration in radial solutions for a system of semilinear elliptic equations Journal of London Mathematical Society 74(2006), no.2, 415-440.
-
(with D'Aprile)
Locating the boundary peaks of least-energy solutions to a
singularly perturbed Dirichlet problem
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Vol. V (2006), 219-259.
- (with Juan D\'avila, Manuel del Pino, Monica Musso )
Singular limits of a two-dimensional boundary value problem
arising in corrosion modelling
Archive Rational Mechanical Analysis 182(2006), no.2, 181-221.
- (with M. del Pino)
Collapsing steady states of the Keller-Segel system
Nonlinearity 19(2006), no.3, 661-684.
- (with M. del Pino and M. Kowalczyk)
Resonance and interior layers in an inhomogeneous phase
transition model . SIAM J. Math. Anal., 38(2006), no.5, 1542-1564.
- (with P. Esposita and A. Pistoia)
Concentrating solutions for Henon equation in R^2
J' Analyse Math. 100(2006), 249-280.
- (with T. Kolokolnikov and M. J. Ward) Zigzag and breakup instabilities of stripes and rings for the two-dimensional Gray-Scott model. Studies in Applied Math. 116(2006), no.1, 35-95.
- (with T. Kolokolnikov, Thomas Erneux)
Mesa-type patterns in the one-dimensional Brusselator and their stability
Physica D: Nonlinear Phenomena 214(2006), no.1, 63-77.
- (with T. Kolokolnikov, M. Ward)
Slow translational instabilities of spike patterns in the one-dimensional Gray-Scott model
Interfaces and Free Boundaries 8(2006), no.2, 185-222.
- (with T. Kolokolnikov, M. Ward)
The Stability of A Stripe for the Gierer-Meinhardt Model and the
Effect of Saturation SIAM J. Applied. Dynamical Systems 5(2006), no.2, 313-363.
- (with ZM Guo)
Hausdorff Dimension of Ruptures for Solutions of a Semilinear
Elliptic Equation with Singular Nonlinearity
Manuscripta Mathematica 120(2006), 193-209.
- (with T.C. Lin)
Spikes in Two-component Systems of Nonlinear
Schr\"{o}dinger Equations with Trapping Potentials
Journal of Differential Equations 229(2006), no.2, 538-569.
- (with TC Lin) Solitary and Self-similar Solutions of Two-component
System of Nonlinear Schr\"{o}dinger Equations . Physica D: Nonlinear Phenomena 220(2006), no. 2, 99-115
- (with TC Lin)
Symbiotic bright solitary wave solutions of coupled nonlinear
Schroedinger equations . Nonlinearity 19(2006), no.12, 2755-2773.
- (with M. Musso) Stationary Solutions to a Keller-Segel Chemotaxis System Asymptotic Analysis, 49(2006), no.3-4, 217-247.,
- (with W.-M. Ni) On positive solutions concentrating on spheres for the Gierer-Meinhardt system J. Diff. Eqns. 221(2006), 158-189.
- (with X. Ren)
Droplet Solutions in the Diblock Copolymer Problem with Skewed
Monomer Composition Cal. Var. and Part. Diff. Eqns. 25(2006), no.3, 333-359.
- (with Xiaofeng Ren)
Existence and Stability of Spherically Layered
Solutions of the Diblock Copolymer Equation
SIAM J. Appl. Math. 66(2006), 1080-1099.
- (with M. Winter)
Standing waves in the FitzHugh-Nagumo system and a problem in combinatorial geometry
Math. Zeit 254(2006), no.2, 359-383.
-
(with S. Yan) Solution Explosant Au Centre Et Le Long Du Bord Pour Un Probl\`{e}me Elliptique
De Neumann Avec Non-Lin\'{e}arit\'e Critique . C. R. Acad. Sci. Paris, 343(2006), no.5, 311-316.
- (with D. Ye and F. Zhou)
Bubbling Solutions for an Anisotropic Emden-Fowler Equation
Comp. Rend. Acad. Sci. Paris 343(2006), no.4, 253-258.
2005
- (with Wenyi Chen)
On Brezis-Nirenberg Problem on $\Sn^3$ and A Conjecture of Bandle-Benguria
Com. Rend. Acad. Sci. Paris 341(2005), no.3, 153-156.
- (with M. del Pino and M. Kowalczyk)
Nonlinear Schr\"odinger equations:
Concentration on weighted geodesics in the semi-classical limit
Comp. Rend. Acad. Sci. Paris 341(2005), no. 4, 223-228.
- (with T. D'Aprile) On bound states
concentrating on spheres for the Maxwell-Schrodinger Equation SIAM J. Math. Anal. 37(2005), no. 1, 321-342.
- (with Theo Kolokolnikov)
On ring-like solutions for the Gray-Scott model: existence, instability
and self-replicating rings Eur. J. Appl. Math., 16(2005), no.2, 201-237.
- (with Theo Kolokolnikov and M.J.Ward)
Pulse-splitting for some reaction-diffusion systems in one-space dimension,
Studies in Appl. Math. 114(2005), no.2, 115-165.
- (with Theo Kolokolnikov and M. Ward)
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the pulse-splitting regime. Physica D: Nonlinear Phenomenon 202(2005), 258-293.
- (with Theo Kolokolnikov and M.J.Ward)
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model, Appl. Math. Letters, 18(2005), no. 8, 951-956.
- (with Theo Kolokolnikov and M. Ward)
The existence and stability of spike equilibria in the one-dimensional Gray-Scott model: the low feed-rate regime. Studies in Appl. Math. 115(2005), no.1, 21-71.
- (with M.E. Hubbard and J. A. Leach) Pattern formation
in a two-dimensional simple chemical system with general orders of autocatalysis and decay. IMA J. Appl. Math., 70(6)(2005), 723-747.
- (with T.-C. Lin) Spikes in two coupled nonlinear Schrodinger equations . Ann. Non linearie, Annoles de l'Institut H. Poincare, 22(2005), no. 4, 403-439.
- (with T.-C. Lin) Ground state of $N$ coupled Nonlinear Schr\"{o}dinger Equations in $R^n, n\leq 3$ Communications in Mathematical Physics 255(3)(2005), 629-653.
- (with W.-M. Ni and A. Malchiodi) Multiple clustered layer solutions for semilinear Neumann problems on
a ball, Ann. Non linearie, Annoles de l'Institut H. Poincare 22(2005), 143-163.
- (with O. Rey) Blowing up Solutions for an Elliptic Neumann Problem with Sub- or Supercritical Nonlinearity. Part II: $N \geq 4$, Ann. Non linearie, Annoles de l'Institut H. Poincare, 22(2005), no. 4, 459-484.
- (with O. Rey)
Arbitrary Number of Positive Solutions For an Elliptic Problem with Critical Nonlinearity. Journal of European Mathematical Society 7(2005), no. 4, 449-476.
- (with X. Ren) Wriggled lamellar solutions and their stability
in the Diblock copolymer problem , SIAM J. Math. Anal. 37(2005), no.2, 455-489.
- (with Xiaofeng Ren) Nucleation in the FitzHugh-Nagumo System: Interface-Spike Solutions Journal of Differential Equations 205(2005), 266-301.
- (with B.D. Sleeman and M.J.Ward)
The existence, stability, and dynamics of spike patterns in a chemotaxsis model , SIAM J. Appl. Math., 65(2005), no. 3, 790-817.
- (with Tobias Weth) On the Number of Nodal Solutions to a Singularly Perturbed Neumann
Problem Manuscripta Mathematica 117(2005), no. 3, 333-344.
- (with M. Winter)
On a cubic-quintic Ginzburg-Landau equation with global coupling, Proceedings of Amer. Math. Soc. 133(2005), no. 6, 1787-1796.
- (with Matthias Winter) Clustered spots in the FitzHugh-Nagumo system Journal of Differential Equations, 213(2005), no.1, 121-145.
- (with M. Winter)
Symmetry of nodal solutions for singularly perturbed elliptic problems on a ball, Indiana Univ. Math. Journal, 54(2005), no. 3, 707-741.
- (with M. Winter and W.K. Yeung) A higher-order energy expansion to two-dimensional singularly
perturbed Neumann problems Asymptotic Analysis, 43(2005), no.1-2, 75-110.
- (with Xingwang Xu)
Uniqueness and a priori estimates for some nonlinear elliptic Neumann equations in $R^3$
Pacific J. Math., 221(2005), no.1, 159-165.
2004
- (with D. Iron and M. Winter)
Stability analysis of Turing patterns generated by the Schnakenberg
model Journal of Math. Biology 49(2004), no.4, 358-390.
- (with O. Rey) Blowing up solutions for an elliptic Neumann
problem with sub- or supercritical nonlinearity I: $N=3$,
Journal of Functional Analysis 212(2004), no.2, 472-499.
- (with X. Ren) Molecular chirality and soliton-stripe pattern in liquid crystal films Nonlinearity 17(2004), Vol. 2, 617-632.
- (with X. Ren) The soliton-stripe pattern in the Seul-Andelman membrane Physica D:Nonlinear Phenomenon 188 (2004), no. 3-4, 277--291.
- (with X. Ren) Stability of spot and ring solutions of the
Diblock copolymer equation Journal of Mathematical Physics 45(2004), no.11, 4106-4133.
- (with M. Winter)
Asymmetric Patterns for the Gierer-Meinhardt system J. Math. Pures Appl. (9)83(2004), no.4, 433-476.
- (with M. Winter)
On Gierer-Meinhardt system with saturation Comm. Contemp. Math. 6(2004), no.2, 259-277.
- (with M. Winter)
Higher order expansions and spike locations Cal. Var. PDE
20(2004), 403-430.
2003
- (with H. Berestycki) On singular perturbation problems with Robin boundary condition, Annali Suola Norm. Sup. Pisa Cl.Sci. (5) Vol.II (2003), 199-230.
- (with del Pino and M. Kowalczyk)
Multi-bump Ground States of the Gierer-Meinhardt system in
$R^2$, Ann. Non linearie, Annoles de l'Institut H. Poincare 20(2003), 53-85.
- (with J. Leach) Pattern
formation in a simple chemical system with general orders of autocatalysis and decay. I. Stability analysis. Physica D:Nonlinear Phenomena 3-4(180)2003, 185-209.
- (with C.S. Lin) Locating the peaks of solutions via the Maximum Principle II: A local version of the method of moving planes. Comm. Pure Appl. Math. 6(2003), 784-809.
- (with X. Ren) Triblock copolymer theory: ordered ABC lamellar phase. Journal of Nonlinear Sciences 13(2003), 175-208.
- (with X. Ren) Triblock copolymer theory: free energy, disordered phase and weak segregation, Physica D:Nonlinear Phenomena 178(2003), 103-117.
- (with X. Ren) On energy minimizers
of the di-block copolymer problem. Interfaces and Free Boundaries 5 (2003), no. 2, 193-238.
- (with X. Ren)
On the spectra of 3-D Lamellar solutions of the Diblock copolymer problem SIAM J. Math. Anal. 35(1)(2003), 1-32.
- (with X. Ren) Soliton-stripe patterns in the charged
Langmuir monolayers Journal of Nonlinear Sciences 13 (2003), no. 6, 603-624.
- (with X. Sun, T. Tang and M. Ward)
Numerical challenges for resolving spike dynamics for two
one-dimensional reaction-diffusion systems, Studies in Appl. Math. 111 (1)(2003), 41-84.
- (with M.J.Ward)
Hopf bifurcations and oscillatory instabilities of spike solutions for the one-dimensional Gierer-Meinhardt model. Journal of Nonlinear Sciences 13(2003), 209-264.
- (with M.J.Ward)
Hopf bifurcations of spike solutions for the shadow Gierer-Meinhardt model Europ. J. Appl. Math. 14 (2003), 677-711.
- (with M. Winter)
Asymmetric spotty patterns for the Gray-Scott model, Studies in Appl. Math. 110(2003), 63-102.
- (with M. Winter)
A nonloal eigenvalue problem and the
stability of spikes for reaction-diffusion systems with fractional
reaction rates, Int. J. Bifur. Chaos 13 (6) (2003), 1529-1543.
- (with M. Winter)
Existence and stability of multiple spot solutions for the Gray-Scott model in $R^2$, Physica D: Nonlinear Phenomena 176(2003), 147-180.
- (with M. Winter) Higher order energy expansions for some singularly perturbed Neumann problems, Comptes Rend de L' Acad. des Sci. I. Math. 337(2003), 37-42.
- (with M. Winter) Stability of monotone solutions for the shadow Gierer-Meinhardt system with finite diffusivity, Diff. Int. Eqns. 16(2003), 1153-1180.
2002
- (with Guofang Wang) Steady State Solutions Of A Reaction-Diffusion System Modeling Chemotaxis, Math. Nach. 233-234(2002), 221-236..
- (with Guofang Wang) On a conjecture of Wolansky, Nonlinear Analysis:TMA 48(2002), 927-937.
- (with S.-I. Ei) Dynamics of metastable localized patterns and
its application to the interaction of spike solutions
for the Gierer-Meinhardt systems in two spatial dimension, Japan J.
Industr. Appl. Math. 19(2002), 181-226
- (with J. Norbury and M. Winter)
Existence and stability of singular patterns
in a Ginzburg-Landau equation coupled with a mean field, Nonlinearity 15(2002), 2077-2096.
- (with X. Ren) Concentrically layered energy equilibria of the di-block copolymer problem, Europ. J. Appl. Math. 13(2002), 479-496.
- (with M. Ward)
Asymmetric Spike Patterns for the One-dimensional Gierer-Meinhardt System: Equilibria and Stability, Europ. J. Appl. Math. 13(2002), 283-320.
- (with M.-J. Ward ) The existence and stability of asymmetric spike patterns for the Schnakenberg
model, Studies in Appl. Math. 109(2002), 229-264.
- (with M. Winter) Spikes for
the Two-Dimensional Gierer-Meinhardt System: The Strong Coupl
ing Case, J. Diff. Eqns. 178(2002), 478-518.
- (with M. Winter) Critical threshold and stability of cluster
solutions for large reaction-diffusion systems in $R^1$,
SIAM J. Math. Anal. 33(2002), 1058-1089.
2001
- Pattern formations in two-dimensional Gray-Scott model: existence of single-spot solutions and their stability, Physica D: Nonlinear Phenomena 148(2001), 1-2, 20-48.
- Uniqueness and critical spectrum of boundary
spike solutions, Proc. Royal Soc. Edin. A 131(2001), 1457-1480.
-
Multiple condensations for a nonlinear elliptic equation with
sub-critical growth and critical behavior, Proc. Edinburgh Math.
Soc. 44(2001), 631-660.
- (with J. Ai and K.S. Chou) Self-similar solutions for
the anisotropic affine curvature shortening problem, Cal. Var. PDE
13 (2001), 311-337.
- (with D. Iron and M.J. Ward) The stability of spike solutions to the one-dimensional Gierer-Meinhardt model, Physica D.: Nonlinear Phenomena 150 (2001), no. 1-2, 25--62.
- (with G. Lu and X. Xu) On Conformally Invariant Equation $ (-\Delta u)^p u-K(x)u^{\frac{N+2p}{N-2p}}=0$ and Its Generalizations, Annali di Mathematica Pura ed Applicata 179(2001), 309-329.
- (with L. Ma) Convergence for a Liouville equation, Comment. Math. Helv. 76(2001), 506-514.
- (with M. Winter)Solutions for the Cahn-Hilliard equation with many boundary spike layers,
Proc. Roy Soc Edinb A 131(2001), 185-204.
- (with M. Winter) Spikes for the
Two-Dimensional Gierer-Meinhardt System: The Weak Coupling Case
Journal of Nonlinear Sciences 6(2001), 415-458.
- (with M. Winter) On a Hypercycle System with Nonlinear Rate, Methods Appl. Anal. 8(2001), 257-278.
-
(with L. Zhang) On a nonlocal eigenvalue problem, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, XXX (2001), 41-62.
2000
- On the effect of the domain geometry in a singularly perturb
ed Dirichlet problem, Diff. Int. Eqns 13(2000), 15-45.
-
On a nonlocal eigenvalue problem and its applications to point-condensations in reaction-diffusion systems, Int. J. Bifurcation and Chaos, Vol. 10 (6) (2000), 1485-1496.
-
(with M. del Pino and Felmer )
On the role of distance function in some singular perturbation pr
oblems,
Comm. PDE 25(2000), 155-177.
-
(with M. Del Pino and P. Felmer ) Mutiple peak solutions for some singular perturbation problems,
Cal. Var. PDE. 10(2000), 119-134.
- (with M. Grossi, A. Pistoia) Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory, Cal. Var. & PDE 11(2000) 143-175.
-
(with C. Gui)
On a sharp Moser-Aubin-Onofri inequality for functions on $S^2
$ with symmetry, Pacific J. Math. 194(2000), 349-358.
-
(with Gui and M. Winter) Mutiple boundary peak solutions for some singularly perturbed Neumann problems,
Ann. Non linearie, Annoles de l'Institut H. Poincare,
, 17(2000), 47-82.
- (with C. Gui) On multiple mixed
interior and boundary peak solutions for some singularly
perturbed Neumann problems, Can. J. Math. 52(2000), 522-538.
- (with Xiaosong Kang)
On interacting bumps of
semiclassical states of nonlinear Schr\"odinger equations,
Adv. Diff. Eqns. Vol. 5 (2000), 899-928.
- (with G. Lu)On a Sobolev inequality with remainder terms, Proceedings of AMS
128(2000), 75-84.
-
(with Xiaofeng Ren) On the
multiplicity of solutions of two nonlocal variational problems, SIAM J. Math. Anal. 31(2000), 909-924.
- (with M. Winter) Multi-Interior-Spike solutions
for the Cahn-Hilliard equation with arbitrarily many peaks, Cal. Var. PDE 10(2000), 249-289.
- (with M. Winter) On a two dimensional reaction-diffusion system with hypercyclical structure, Nonlinearity 13(2000), 2005-2032.
1999
- Point condensations of a model for fungal development,
C. R. Acad. Sci. Paris 328(1999), 129-134.
- Existence, stability and metastability of point condensation patterns generated by Gray-Scott System Nonlinearity 12(1999), 593-616.
- On single interior spike solutions of Gierer-Meinhardt system: uniqueness,
spectrum estimates,
Europ. J. Appl. Math. 10(1999), 353-378.
- (with E.N.Dancer) On the location
of spikes and profile of solutions with two sharp layers, J. Diff. Eqns. 157(1999), 82-101.
- (with M. del Pino and Felmer )
On the role of mean curvature in some singularly perturbed
Neumann problems, SIAM J. Math. Anal. 31 (1999), 63-79.
- (with C. Gui)
Mutiple interior peak solutions for some singularly perturbed Neumann problems,
J. Diff. Eqns. 158(1999), 1-27.
- (with Xuefeng Wang) Shift and stability of ground states of a nonlinear Schr\"odinger equation outside
a small insulated domain, J. Diff. Eqns. 154(1999), 73-95.
- (with Winter) Multiple-peak solutions for a wide class of sing
ular perturbation problems, J. London Math. Soc. 59(2)(1999), 585-606.
- (with M. Winter)
On the two dimensional Gierer-Meinhardt system with strong coupling,
SIAM J. Math. Anal. 30(1999), 1241-1243.
- (with Xingwang Xu)
Classification of solutions of high order conformally invariant equations,
Math. Annalen 313(2)(1999), 207-228.
1998
- Asymptotic behavior of least-energy solutions of a semilinear
Dirichlet problem involving critical Sobolev exponent, J. Math. Soc.
of Japan , Vol 1 (1998), 139-153.
- On the interior spike layer solutions of a singularly perturbed
semilinear Neumann problem, Tohoku Math. J. , Vol. 50 (2), 1998, 159-178.
- Conditions for two-peaked solutions of singularly perturbed elliptic equations,
Manuscripta Mathematica , 96(1998), 113-136.
- On the interior spike layer solutions for some singular perturbation problems, Proc. Royal
Soc. Edinburgh, Section A (Mathematics) , 128 (1998), 849-874.
- (with G. Cerami) Multiplicity of multiple interior spike solutions for some singularly perturbed Neumann problem,
International Mathematics Research Notes , 12(1998), 601-626.
- (with E.N.Dancer) On the effect of domain topology in some singular perturbation problems,
Topological Methods in Nonlinear Analysis 11(2) (1998), 227-248.
- (with M. Flucher) Asymptotic behavior of elliptic free boundary
problem, Math. Zeit 228(1998), 683-703.
- (with G. Lu) On Nonlinear Schrodinger Equations With Totally Degenerate Potentials,
C. R. Acad. Sci. Paris, , 326(1998), 691-696.
- (with E. Noussair ) On the existence and profile of nodal solutions of some singularly perturbed
semilinear Neumann problem, Comm. Partial Diff. Eqns. , 23(1998), 793-816.
- (with W.-M. Ni and I. Takagi) On the location and profile of sp
ike-layer solutions to singularly perturbed semilinear Dirichlet problems:
intermediate solutions, Duke Math. J. 94 (1998), 597-618.
- (with M. Winter ) Stationary solutions of Cahn-Hilliard equation,
Ann. Non linearie, Annoles de l'Institut H. Poincare 15 (1998), 459-492.
- (with M. Winter ) On the Cahn-Hilliard equations II: interior spike Layer solutions,
J. Diff. Eqns. 148(1998), 231-267.
- (with M. Winter) On the stationary Cahn-Hilliard equation:
Bubble solutions, SIAM Journal on Mathematical Analysis 29(1998), 1492-1518.
- (with Xingwang Xu)On Conformal Deformations of Metrics On $S^n$
J. Functional Analysis , 157(1998), 292-325.
1997
- On the boundary spike layer solutions of a singularly perturbed
semilinear Neumann problem, J. Diff. Eqns, 134 (1997), 104-133.
- Exact Multiplicity for Some Nonlinear Elliptic Equations in Balls,
Proc. Amer. Math. Soc., 125 (1997), No. 11, 3235-3242.
- (with Dancer) On the profile of solutions with two sharp layers
to a singularly perturbed semilinear Dirichlet problem, Proc. Royal
Soc. Edinburgh, Section A (Mathematics), 127 A(1997), 691-701.
- (with M. Flucher) Semilinear Dirichlet problem with nearly critical exponent, asymptotic location of hot spots,
Manuscript. Math. 94 (1997), 337-346.
- (with G. Lu) On positive entire solutions to the Yamabe-type problem on
the Heisenberg and stratified groups, Electronic Research Announcements of American Mathematical Society
, 3(1997), 83-89.
- (with E. Noussair ) On the effect of domain geometry on the exist
ence and profile of nodal solutions of some singularly perturbed semilinear Dirichlet problem,
Indiana Univ. Math. J. , 46(1997), 1255-1272.
1996
- On construction of single-peak spiky solutions
to singularly perturbed semilinear Dirichlet problems, J. Diff. Eqns.
129 (2) 1996, 315-333.
- Asymptotic behavior of a nonlinear fourth order eigenvalue problem, Comm. Part. Diff. Eqns. , 21 (1996), 1451-1468.
- (with X. Ren) Single-point condensation and least energy solutions,
Proc. Amer. Math. Soc, 124 (1) 1996, 111-120.
1995
- (with W.-M. Ni) On the location and profile of spike-layer
solutions to singularly perturbed semilinear Dirichlet problems,
Comm. Pure Appl. Math. , 48(1995), 723-761.
- (with X. Ren) Counting peaks of solutions to some quasilinear
elliptic equations with large exponent,
J. Diff. Eqn., 117(1995), 28-55.
- (with X. Ren) Asymptotic behavior of least energy solutions to
a two dimensional semilinear problem with mixed boundary condition,
Nonlinear Analysis: Theory, Methods and Applications, 24(4) 1995, 587-6
04.
- (with X. Ren) On a semilinear equation in $R^{2}$ when the exponent approaches infinity,
J. Math. Anal. Appl., 189(1995), 179-193.
- (with X. Wang) On the equation
$ \Delta u + K(x) u^{\frac{n+2}{n-2} \pm \epsilon^{2}}=0$ in
$ R^{n} $, Rendiconti Del Circolo Matematico Di Palermo , XLIV (1995), 1-37.
1994
- (with X. Ren) On a two dimensional elliptic problem with large exponent in nonlinearity, Trans. Amer. Math. Soc. , 343 (2) 1994, 749-763.
Publications in Proceedings of Conference as Invited Talks:
- On the effect of domain geometry and boundary geometry in some singular perturbation problems, Differential Equations and Applications (P. Bates ed.) , International Press, 1998,326-339.
- On the construction of interior spike layer solutions to a singularly perturbed semilinear Neumann problem,
PARTIAL DIFFERENTIAL EQUATIONS:THEORY AND NUMERICAL SOLUTION ,
CRC Press LLC, 1998, 336-349.
- Existence and Stability of Spikes for the Gierer-Meinhardt System (99 Pages) HANDBOOK OF DIFFERENTIAL EQUATIONS, stationary partial differential equations, volume 5 (M. Chipot ed.) , Elservier. pp. 489-581.
- Geometrization Program of Semilinear Elliptic Equations 2010 ICCM Proceedings AMS/IP Studies in Advanced Mathematics
.
Book
- (with M. Winter) Mathematical Aspects of Pattern Formation in Biological Systems
Applied Mathematical Sciences Series, Vol. 189,
Springer 2014 , ISBN: 978-4471-5525-6.
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