Publication List

Publications in Refereed Journals:

  1. (with X. Ren) On a two dimensional elliptic problem with large exponent in nonlinearity, Trans. Amer. Math. Soc. , 343 (2) 1994, 749-763.
  2. (with X. Ren) Counting peaks of solutions to some quasilinear elliptic equations with large exponent, J. Diff. Eqn., 117(1995), 28-55.
  3. (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.
  4. (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.
  5. (with X. Ren) On a semilinear equation in $R^{2}$ when the exponent approaches infinity, J. Math. Anal. Appl., 189(1995), 179-193.
  6. (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.
  7. On construction of single-peak spiky solutions to singularly perturbed semilinear Dirichlet problems, J. Diff. Eqns. 129 (2) 1996, 315-333.
  8. Asymptotic behavior of a nonlinear fourth order eigenvalue problem, Comm. Part. Diff. Eqns. , 21 (1996), 1451-1468.
  9. (with X. Ren) Single-point condensation and least energy solutions, Proc. Amer. Math. Soc, 124 (1) 1996, 111-120.
  10. On the boundary spike layer solutions of a singularly perturbed semilinear Neumann problem, J. Diff. Eqns, 134 (1997), 104-133.
  11. (with M. Flucher) Semilinear Dirichlet problem with nearly critical exponent, asymptotic location of hot spots, Manuscript. Math. 94 (1997), 337-346.
  12. Exact Multiplicity for Some Nonlinear Elliptic Equations in Balls, Proc. Amer. Math. Soc., 125 (1997), No. 11, 3235-3242.
  13. (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.
  14. (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.
  15. 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.
  16. (with G. Lu) On Nonlinear Schrodinger Equations With Totally Degenerate Potentials, C. R. Acad. Sci. Paris, , 326(1998), 691-696.
  17. On the interior spike layer solutions of a singularly perturbed semilinear Neumann problem, Tohoku Math. J. , Vol. 50 (2), 1998, 159-178.
  18. Conditions for two-peaked solutions of singularly perturbed elliptic equations, Manuscripta Mathematica , 96(1998), 113-136.
  19. (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.
  20. (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.
  21. (with G. Cerami) Multiplicity of multiple interior spike solutions for some singularly perturbed Neumann problem, International Mathematics Research Notes , 12(1998), 601-626.
  22. (with M. Winter ) Stationary solutions of Cahn-Hilliard equation , Ann. Non linearie, Annoles de l'Institut H. Poincare 15 (1998), 459-492.
  23. (with Xingwang Xu) On Conformal Deformations of Metrics On $S^n$ J. Functional Analysis , 157(1998), 292-325.
  24. On the interior spike layer solutions for some singular perturbation problems, Proc. Royal Soc. Edinburgh, Section A (Mathematics) , 128 (1998), 849-874.
  25. (with M. Winter ) On the Cahn-Hilliard equations II: interior spike Layer solutions, J. Diff. Eqns. 148(1998), 231-267.
  26. (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.
  27. (with M. Winter) On the stationary Cahn-Hilliard equation: Bubble solutions, SIAM Journal on Mathematical Analysis 29(1998), 1492-1518.
  28. (with M. Flucher) Asymptotic behavior of elliptic free boundary problem, Math. Zeit 228(1998), 683-703.
  29. (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.
  30. Point condensations of a model for fungal development, C. R. Acad. Sci. Paris 328(1999), 129-134.
  31. (with Xingwang Xu) Classification of solutions of high order conformally invariant equations, Math. Annalen 313(2)(1999), 207-228.
  32. (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.
  33. Existence, stability and metastability of point condensation patterns generated by Gray-Scott System, Nonlinearity 12(1999), 593-616.
  34. (with Winter) Multiple-peak solutions for a wide class of sing ular perturbation problems, J. London Math. Soc. 59(2)(1999), 585-606.
  35. (with E.N.Dancer) On the location of spikes and profile of solutions with two sharp layers, J. Diff. Eqns. 157(1999), 82-101.
  36. On single interior spike solutions of Gierer-Meinhardt system: uniqueness, spectrum estimates, Europ. J. Appl. Math. 10(1999), 353-378.
  37. (with C. Gui) Mutiple interior peak solutions for some singularly perturbed Neumann problems, J. Diff. Eqns. 158(1999), 1-27.
  38. (with M. Winter) On the two dimensional Gierer-Meinhardt system with strong coupling, SIAM J. Math. Anal. 30(1999), 1241-1243.
  39. (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.
  40. (with G. Lu) On a Sobolev inequality with remainder terms, Proceedings of AMS 128(2000), 75-84.
  41. On the effect of the domain geometry in a singularly perturb ed Dirichlet problem, Diff. Int. Eqns 13(2000), 15-45.
  42. (with M. Winter and Gui) Mutiple boundary peak solutions for some singularly perturbed Neumann problems, Ann. Non linearie, Annoles de l'Institut H. Poincare, , 17(2000), 47-82.
  43. (with M. del Pino and Felmer ) On the role of distance function in some singular perturbation pr oblems, Comm. PDE 25(2000), 155-177.
  44. (with M. Del Pino and P. Felmer ) Mutiple peak solutions for some singular perturbation problems, Cal. Var. PDE. 10(2000), 119-134.
  45. (with C. Gui) On a sharp Moser-Aubin-Onofri inequality for functions on $S^2 $ with symmetry, Pacific J. Math. 194(2000), 349-358.
  46. (with C. Gui) On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems, Can. J. Math. 52(2000), 522-538.
  47. (with M. Winter) Multi-Interior-Spike solutions for the Cahn-Hilliard equation with arbitrarily many peaks, Cal. Var. PDE 10(2000), 249-289.
  48. (with Xiaofeng Ren) On the multiplicity of solutions of two nonlocal variational problems, SIAM J. Math. Anal. 31(2000), 909-924.
  49. 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.
  50. (with Kang Xiaosong) On interacting bumps of semiclassical states of nonlinear Schr\"odinger equations, Adv. Diff. Eqns. Vol. 5 (2000), 899-928.
  51. (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.
  52. (with M. Winter) On a two dimensional reaction-diffusion system with hypercyclical structure, Nonlinearity 13(2000), 2005-2032.
  53. (with M. Winter)Solutions for the Cahn-Hilliard equation with many boundary spike layers, Proc. Roy Soc Edinb A 131(2001), 185-204.
  54. 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.
  55. (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.
  56. (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.
  57. (with L. Ma) Convergence for a Liouville equation, Comment. Math. Helv. 76(2001), 506-514.
  58. (with L. Zhang) On a nonlocal eigenvalue problem, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, XXX (2001), 41-62.
  59. (with J. Ai and K.S. Chou) Self-similar solutions for the anisotropic affine curvature shortening problem, Cal. Var. PDE 13 (2001), 311-337.
  60. Uniqueness and critical spectrum of boundary spike solutions, Proc. Royal Soc. Edin. A 131(2001), 1457-1480.
  61. Multiple condensations for a nonlinear elliptic equation with sub-critical growth and critical behavior, Proc. Edinburgh Math. Soc. 44(2001), 631-660.
  62. (with M. Winter) Spikes for the Two-Dimensional Gierer-Meinhardt System: The Weak Coupling Case Journal of Nonlinear Sciences 6(2001), 415-458.
  63. (with M. Winter) On a Hypercycle System with Nonlinear Rate, Methods Appl. Anal. 8(2001), 257-278.
  64. (with Guofang Wang) Steady State Solutions Of A Reaction-Diffusion System Modeling Chemotaxis, Math. Nach. 233-234(2002), 221-236..
  65. (with Guofang Wang) On a conjecture of Wolansky, Nonlinear Analysis:TMA 48(2002), 927-937.
  66. (with M. Winter) Spikes for the Two-Dimensional Gierer-Meinhardt System: The Strong Coupl ing Case, J. Diff. Eqns. 178(2002), 478-518.
  67. (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.
  68. (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
  69. (with M. Ward) Asymmetric Spike Patterns for the One-dimensional Gierer-Meinhardt System: Equilibria and Stability, Europ. J. Appl. Math. 13(2002), 283-320.
  70. (with M.-J. Ward ) The existence and stability of asymmetric spike patterns for the Schnakenberg model, Studies in Appl. Math. 109(2002), 229-264.
  71. (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.
  72. (with X. Ren) Concentrically layered energy equilibria of the di-block copolymer problem, Europ. J. Appl. Math. 13(2002), 479-496.
  73. (with M. Winter) Asymmetric spotty patterns for the Gray-Scott model, Studies in Appl. Math. 110(2003), 63-102.
  74. (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.
  75. (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.
  76. (with X. Ren) Triblock copolymer theory: free energy, disordered phase and weak segregation, Physica D:Nonlinear Phenomena 178(2003), 103-117.
  77. (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.
  78. (with X. Ren) Triblock copolymer theory: ordered ABC lamellar phase. Journal of Nonlinear Sciences 13(2003), 175-208.
  79. (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.
  80. (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.
  81. (with X. Ren) On energy minimizers of the di-block copolymer problem. Interfaces and Free Boundaries 5 (2003), no. 2, 193-238.
  82. (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.
  83. (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.
  84. (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.
  85. (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.
  86. (with H. Berestycki) On singular perturbation problems with Robin boundary condition, Annali Suola Norm. Sup. Pisa Cl.Sci. (5) Vol.II (2003), 199-230.
  87. (with X. Ren) Molecular chirality and soliton-stripe pattern in liquid crystal films Nonlinearity 17(2004), Vol. 2, 617-632.
  88. (with M. Winter) Stability of monotone solutions for the shadow Gierer-Meinhardt system with finite diffusivity, Diff. Int. Eqns. 16(2003), 1153-1180.
  89. (with M.J.Ward) Hopf bifurcations of spike solutions for the shadow Gierer-Meinhardt model Europ. J. Appl. Math. 14 (2003), 677-711.
  90. (with X. Ren) Soliton-stripe patterns in the charged Langmuir monolayers Journal of Nonlinear Sciences 13 (2003), no. 6, 603-624.
  91. (with X. Ren) The soliton-stripe pattern in the Seul-Andelman membrane Physica D:Nonlinear Phenomenon 188 (2004), no. 3-4, 277--291.
  92. (with M. Winter) Asymmetric Patterns for the Gierer-Meinhardt system J. Math. Pures Appl. (9)83(2004), no.4, 433-476.
  93. (with M. Winter) On Gierer-Meinhardt system with saturation Comm. Contemp. Math. 6(2004), no.2, 259-277.
  94. (with M. Winter) Higher order expansions and spike locations Cal. Var. PDE 20(2004), 403-430.
  95. (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.
  96. (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.
  97. (with Xiaofeng Ren) Stability of spot and ring solutions of the Diblock copolymer equation Journal of Mathematical Physics 45(2004), no.11, 4106-4133.
  98. (with Xiaofeng Ren) Nucleation in the FitzHugh-Nagumo System: Interface-Spike Solutions Journal of Differential Equations 205(2005), 266-301.
  99. (with M. Winter) On a cubic-quintic Ginzburg-Landau equation with global coupling, Proceedings of Amer. Math. Soc. 133(2005), no. 6, 1787-1796.
  100. (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.
  101. (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.
  102. (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.
  103. (with T.-C. Lin) $N$ coupled Nonlinear Schr\"{o}dinger Equations]{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.
  104. (with Xingwang Xu) Uniqueness and a priori estimates for some nonlinear elliptic Neumann equations in $R^3$ Pacific J. Math., accepted for publication
  105. (with M. Winter) Symmetric and asymmetric clusters in an elliptic system. NoDEA, accepted for publication.
  106. (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.
  107. (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.
  108. (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.
  109. (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.
  110. (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.
  111. (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.
  112. (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.
  113. (with Matthias Winter) Clustered spots in the FitzHugh-Nagumo system Journal of Differential Equations, 213(2005), no.1, 121-145.
  114. (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.
  115. (with T. D'Aprile) Standing waves in the Maxwell-Schrodinger qquation and an optimal configuration problem. Cal. Var. and PDE, 25(2006), 105-137.
  116. (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.
  117. (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.
  118. (with X. Ren) Wriggled lamellar solutions and their stability in the Diblock copolymer problem , SIAM J. Math. Anal. 37(2005), no.2, 455-489.
  119. (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.
  120. (with W.-M. Ni) On positive solutions concentrating on spheres for the Gierer-Meinhardt system J. Diff. Eqns. 221(2006), 158-189.
  121. (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.
  122. (with Tobias Weth) On the Number of Nodal Solutions to a Singularly Perturbed Neumann Problem Manuscripta Mathematica 117(2005), no. 3, 333-344.
  123. (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.
  124. (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.
  125. (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.
  126. (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.
  127. (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.
  128. (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 accepted for publication.
  129. (with Xiaofeng Ren) Existence and Stability of Spherically Layered Solutions of the Diblock Copolymer Equation SIAM J. Appl. Math. 66(2006), 1080-1099.
  130. (with M. Winter) Standing waves in the FitzHugh-Nagumo system and a problem in combinatorial geometry Math. Zeit accepted for publication.
  131. (with D'Aprile) Layered solutions for a semilinear elliptic system in a ball J. Diff. Eqns. 226(2006), 269-294.
  132. (with D. Ye and F. Zhou) Bubbling Solutions for an Anisotropic Emden-Fowler Equation Cal. Var. and Part. Diff. Eqns. 28(2007), 217-247.
  133. (with T. D'Aprile) Boundary Concentration in radial solutions for a system of semilinear elliptic equations Journal of London Mathematical Society accepted for publication.
  134. (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.
  135. (with M. del Pino) Collapsing steady states of the Keller-Segel system Nonlinearity 19(2006), no.3, 661-684.
  136. (with T.C. Lin) Spikes in Two-component Systems of Nonlinear Schr\"{o}dinger Equations with Trapping Potentials Journal of Differential Equations accepted for publication.
  137. (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.
  138. (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.
  139. (with ZM Guo) Hausdorff Dimension of Ruptures for Solutions of a Semilinear Elliptic Equation with Singular Nonlinearity Manuscripta Mathematica 120(2006), 193-209.
  140. (with M. Musso) Stationary Solutions to a Keller-Segel Chemotaxis System Asymptotic Analysis, 49(2006), no.3-4, 217-247.,
  141. (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.
  142. (with P. Esposita and A. Pistoia) Concentrating solutions for Henon equation in R^2 J' Analyse Math. 100(2006), 249-280.
  143. (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
  144. (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.
  145. (with A. Malchiodi and W.-M. Ni) Boundary Clustered Interfaces for Allen Cahn Equation . Pacific Journal of Mathematics , 229(2007), no.2, 447-468.
  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.
  147. (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
  148. (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.
  149. (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.
  150. (with M. del Pino and M. Kowalczyk) Resonance and interior layers in an inhomogeneous phase transition model . SIAM J. Math. Anal., 38(2006/2007), no.5, 1542-1564.
  151. (with TC Lin) Symbiotic bright solitary wave solutions of coupled nonlinear Schroedinger equations . Nonlinearity 19(2006), no.12, 2755-2773.
  152. (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.
  153. (with S. Yan) Lazer-Mckenna conjecture: the critical case . Journal of Functional Analysis 244(2007), 639-667.
  154. (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), accepted for publication.
  155. (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.
  156. (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.
  157. (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.
  158. (with Manuel del Pino and Mike Kowalczyk ) The Toda system and clustering interfaces in the Allen-Cahn equation Archive Rational Mechanical Analysis accepted for publication.
  159. (with Th. Kolokolnikov and Michael Ward ) Self-replication of mesa patterns in reaction-diffusion systems, Physica D: Nonlinear Phenomena accepted for publication.
  160. (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, accepted for publication.
  161. (with Tobias Weth ) Radial solutions and phase separation in a system of two coupled Schr\"odinger equations, Archive Rational Mechanical Analysis accepted for publication.
  162. (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.
  163. (with A. Malchiodi) Boundary Interface for the Allen-Cahn Equation Journal of Fixed Point Theory and Applications (JFPTA) 1(2007), no.2, 305-336.
  164. (with S. Yan) New Solutions For Nonlinear Schr\"odinger Equations with critical nonlinearity . Journal of Differential Equations 237(2007), no.2, 446-472.
  165. (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.
  166. (with F.Mahmoudi and A. Malchiodi) Transition Layer for the Heterogeneous Allen-Cahn Equation Ann. Non linearie, Annoles de l'Institut H. Poincare, accepted for publication.
  167. (with C. Bandle) Nonradial Clustered Spike Solutions for Semilinear Elliptic Problems on $S^n$ J' Analyse Math. 102(2007), 181-208.
  168. (with E.Dancer) Sign-changing solutions for supercritical elliptic problems in domains with small holes Manuscripta Mathematica 123(2007), no.4, 493-511.
  169. (with Xiaofeng Ren) Single droplet pattern in the cylindrical phase of diblock copolymer morphology Journal of Nonlinear Science 17(2007), no.5, 471-503
  170. (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.
  171. (with Guo ZM) On the Cauchy problem for a reaction-diffusion equation with a singular nonlinearity J. Diff. Eqns. 240(2007), 181-208.
  172. (with X. Ren) The critical mass constraint in the Cahn-Hilliard equation Interfaces and Free Boundary Problems accepted for publication.
  173. (with X. Ren) Many droplet pattern in the cylindrical phase of diblock copolymer morphology Reviews in Mathematical Physics 19(2007), no.8, 879-921.
  174. (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. .
  175. (with YH Ding) Semiclassical states for nonlinear Schrodinger equations with sign-changing potentials Journal of Functional Analysis 251(2007), no.2, 546-572.
  176. (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.
  177. (with F. Robert) Asymptotic behavior of a fourth order equation with Dirichlet boundary condition Indiana Univ. Math. J. accepted for publication.
  178. (with M. Winter) Stationary Multiple Spots for Reaction-Diffusion Systems Journal of Mathematical Biology 57(2008), no.1, 53-89.
  179. (with YX Guo) Supercritical biharmonic elliptic problems in domains with small holes Math. Nach. accepted for publication.
  180. (with TC Lin) Orbital stability of bound states of semi-classical nonlinear Schr\"{o}dinger equations with critical nonlinearity SIAM J. Mathematical Analysis accepted for publication.
  181. (with Li Ma) Properties of positive solutions to an Elliptic Equation with negative exponent Journal of Functional Analysis 254(2008), no.4, 1058-1087.
  182. (with T. Bartsch and Zhi-qiang Wang) Bound states for a coupled nonlinear Schrodinger system JFPTA 2(2007), no.2, 353-367.
  183. (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.
  184. (with Dong Ye) Nonradial solutions for a conformally invariant fourth order equation in $R^4$ Cal. Var. PDE 32(2008), no.3, 373-386.
  185. (with ZM Guo) Asymptotic Behavior of touch-down solutions and global bifurcations for an elliptic problem with a singular nonlinearity Comm. Pure Appl. Anal. accepted for publication.
  186. (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.
  187. (with Jun Yang) Toda system and interior clustering line concentration for a singularly perturbed Neumann problem in two dimensional domain DCDS-A accepted for publication.
  188. (with ZM Guo) Infinitely many turning points for an elliptic problem with a singular nonlinearity Journal of London Mathematical Society, accepted for publication.
  189. (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 accepted for publication.
  190. (with T. Weth) Asymptotic behavior of solutions of planar elliptic systems with strong competition Nonlinearity 21(2008), no.2, 305-317.
  191. (with E.N. Dancer) Spike Solutions in coupled nonlinear Schr\"odinger equations with Attractive Interaction Transc. American Math. Soc. accepted for publication.
  192. (with Z.M. Guo) Entire solutions and global bifurcations for a biharmonic equation with singular nonlinearity in $\mathbb R^3$ Adv. Diff. Eqns. accepted for publication.
  193. (with M. Winter) Existence, Classification and Stability Analysis of Multiple-peaked Solutions for the Gierer-Meinhardt System in $R^1$ Methods Appl. Anal. accepted for publication.
  194. (with Theodore Kolokolnikov and M. Ward) Spot self-replication and dynamics for the Schnakenburg model in a two-dim ensional domain Journal of Nonlinear Science accepted for publication.
  195. (with P. Esposito) Non-simple Blow-up Solutions for the Neumann two-dimensional $\sinh-$Gordon equation Cal Var. PDE accepted for publication.
  196. (with Theodore Kolokolnikov) Positive Clustered Layered Solutions For the Gierer-Meinhardt System Journal of Differential Equations accepted for publication.
  197. (with M. Winter) Mutually Exclusive Spiky Pattern and Segmentation Modeled by the Five-Component Meinhardt-Gierer System SIAM J. Appl. Math. accepted for publication.

Publications in Proceedings of Conference as Invited Talks:

  1. 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.
  2. 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.
  3. 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.
    4. .

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