Multiple clustered layer solutions for semilinear Neumann problems on a ball

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 22, Issue 2, 2005, Pages 143-163

  Malchiodi, A ^a   Ni, Wei Ming ^b   Wei, Juncheng ^c  

^a SISSA   (Italy)

^b UNIVERSITY OF MINNESOTA   (United States)

^c CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Multiple clustered layers; Singularly perturbed Neumann problem

Indexed keywords

INTEGER PROGRAMMING; LAPLACE TRANSFORMS; MATHEMATICAL OPERATORS; PERTURBATION TECHNIQUES; PROBLEM SOLVING; THEOREM PROVING;

LAPLACE OPERATOR; MULTIPLE CLUSTERED LAYERS; PATTERN FORMATION; SINGULARITY PERTURBED NEUMANN PROBLEM;

BOUNDARY VALUE PROBLEMS;

EID: 13844306817     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2004.05.003     Document Type: Article

References (33)

1. A. Ambrosetti, A. Malchiodi, and W.-M. Ni Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I Comm. Math. Phys. 235 2003 427 466
2. A. Ambrosetti, A. Malchiodi, and W.-M. Ni Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part II Indiana Univ. Math. J. 53 2004 297 329
3. P. Bates, and G. Fusco Equilibria with many nuclei for the Cahn-Hilliard equation J. Differential Equations 160 2000 283 356
4. P. Bates, E.N. Dancer, and J. Shi Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability Adv. Differential Equations 4 1999 1 69
5. C.C. Chen, and C.S. Lin Uniqueness of the ground state solution of Δ u + f (u) = 0 in R N, N ≥ 3 Comm. PDE 16 1991 1549 1572
6. M. del Pino, and P. Felmer Spike-layered solutions of singularly perturbed elliptic problems in a degenerate setting Indiana Univ. Math. J. 48 3 1999 883 898
7. M. del Pino, P. Felmer, and M. Musso Two-bubble solutions in the super-critical Bahri-Coron's problem Cal. Var. PDE 16 2 2003 113 145
8. M. del Pino, P. Felmer, and J. Wei On the role of mean curvature in some singularly perturbed Neumann problems SIAM J. Math. Anal. 31 1999 63 79
9. M. del Pino, P. Felmer, and J. Wei On the role of distance function in some singularly perturbed problems Comm. PDE 25 2000 155 177
10. M. del Pino, P. Felmer, and J. Wei Mutiple peak solutions for some singular perturbation problems Cal. Var. PDE 10 2000 119 134
11. E.N. Dancer, and S. Yan Multipeak solutions for a singular perturbed Neumann problem Pacific J. Math. 189 1999 241 262
12. E.N. Dancer, and S. Yan Multi-layer solutions for an elliptic problem J. Differential Equations 194 2003 382 405
13. C. Gui, and J. Wei Multiple interior spike solutions for some singular perturbed Neumann problems J. Differential Equations 158 1999 1 27
14. C. Gui, and J. Wei On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems Can. J. Math. 52 2000 522 538
15. C. Gui, J. Wei, and M. Winter Multiple boundary peak solutions for some singularly perturbed Neumann problems Ann. Inst. H. Poincaré Anal. Non Linéaire 17 2000 249 289
16. M. Grossi, A. Pistoia, and J. Wei Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory Cal. Var. PDE 11 2000 143 175
17. Y.-Y. Li On a singularly perturbed equation with Neumann boundary condition Comm. PDE 23 1998 487 545
18. Y.-Y. Li, and L. Nirenberg The Dirichlet problem for singularly perturbed elliptic equations Comm. Pure Appl. Math. 51 1998 1445 1490
19. C.-S. Lin, W.-M. Ni, and I. Takagi Large amplitude stationary solutions to a chemotaxis systems J. Differential Equations 72 1988 1 27
20. A. Malchiodi, and M. Montenegro Boundary concentration phenomena for a singularly perturbed elliptic problem Comm. Pure Appl. Math. 55 2002 1507 1508
21. K. Nakashima, and K. Tanaka Clustering layers and boundary layers in spatially inhomogeneous phase transition problems AIHP Analyse Nonlineaire 20 1 2003 107 143
22. W.-M. Ni Diffusion, cross-diffusion, and their spike-layer steady states Notices Amer. Math. Soc. 45 1998 9 18
23. W.-M. Ni, and I. Takagi On the shape of least energy solution to a semilinear Neumann problem Comm. Pure Appl. Math. 41 1991 819 851
24. W.-M. Ni, and I. Takagi Locating the peaks of least energy solutions to a semilinear Neumann problem Duke Math. J. 70 1993 247 281
25. W.-M. Ni, and I. Takagi Point-condensation generated by a reaction-diffusion system in axially symmetric domains Japan J. Industrial Appl. Math. 12 1995 327 365
26. W.-M. Ni, I. Takagi, and J. Wei On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems: intermediate solutions Duke Math. J. 94 1998 597 618
27. W.-M. Ni, and J. Wei On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems Comm. Pure Appl. Math. 48 1995 731 768
28. J. Wei On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem J. Differential Equations 129 1996 315 333
29. J. Wei On the boundary spike layer solutions of singularly perturbed semilinear Neumann problem J. Differential Equations 134 1997 104 133
30. J. Wei On the interior spike layer solutions to a singularly perturbed Neumann problem Tohoku Math. J. 50 1998 159 178
31. J. Wei On the effect of the domain geometry in a singularly perturbed Dirichlet problem Differential Integral Equations 13 2000 15 45
32. J. Wei, and M. Winter Stationary solutions for the Cahn-Hilliard equation Ann. Inst. H. Poincaré Anal. Non Linéaire 15 1998 459 492
33. J. Wei, and M. Winter Multiple boundary spike solutions for a wide class of singular perturbation problems J. London Math. Soc. 59 1999 585 606