Multiple clustered layer solutions for semilinear Neumann problems on a ball
Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 2, pp. 143-163. 
@article{AIHPC_2005__22_2_143_0,
     author = {Malchiodi, A. and Ni, Wei-Ming and Wei, Juncheng},
     title = {Multiple clustered layer solutions for semilinear {Neumann} problems on a ball},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {143--163},
     publisher = {Elsevier},
     volume = {22},
     number = {2},
     year = {2005},
     doi = {10.1016/j.anihpc.2004.05.003},
     mrnumber = {2124160},
     zbl = {02165096},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2004.05.003/}
}
TY  - JOUR
AU  - Malchiodi, A.
AU  - Ni, Wei-Ming
AU  - Wei, Juncheng
TI  - Multiple clustered layer solutions for semilinear Neumann problems on a ball
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2005
SP  - 143
EP  - 163
VL  - 22
IS  - 2
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2004.05.003/
DO  - 10.1016/j.anihpc.2004.05.003
LA  - en
ID  - AIHPC_2005__22_2_143_0
ER  - 
%0 Journal Article
%A Malchiodi, A.
%A Ni, Wei-Ming
%A Wei, Juncheng
%T Multiple clustered layer solutions for semilinear Neumann problems on a ball
%J Annales de l'I.H.P. Analyse non linéaire
%D 2005
%P 143-163
%V 22
%N 2
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2004.05.003/
%R 10.1016/j.anihpc.2004.05.003
%G en
%F AIHPC_2005__22_2_143_0
Malchiodi, A.; Ni, Wei-Ming; Wei, Juncheng. Multiple clustered layer solutions for semilinear Neumann problems on a ball. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 2, pp. 143-163. doi : 10.1016/j.anihpc.2004.05.003. http://www.numdam.org/articles/10.1016/j.anihpc.2004.05.003/

[1] Ambrosetti A., Malchiodi A., Ni W.-M., Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part I, Comm. Math. Phys. 235 (2003) 427-466. | MR | Zbl

[2] Ambrosetti A., Malchiodi A., Ni W.-M., Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres, Part II, Indiana Univ. Math. J. 53 (2004) 297-329. | MR | Zbl

[3] Bates P., Fusco G., Equilibria with many nuclei for the Cahn-Hilliard equation, J. Differential Equations 160 (2000) 283-356. | MR | Zbl

[4] Bates P., Dancer E.N., Shi J., Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability, Adv. Differential Equations 4 (1999) 1-69. | MR | Zbl

[5] Chen C.C., Lin C.S., Uniqueness of the ground state solution of Δu+fu=0 in R N ,N≥3, Comm. PDE 16 (1991) 1549-1572. | MR | Zbl

[6] Del Pino M., Felmer P., Spike-layered solutions of singularly perturbed elliptic problems in a degenerate setting, Indiana Univ. Math. J. 48 (3) (1999) 883-898. | MR | Zbl

[7] Del Pino M., Felmer P., Musso M., Two-bubble solutions in the super-critical Bahri-Coron's problem, Cal. Var. PDE 16 (2) (2003) 113-145. | MR | Zbl

[8] Del Pino M., Felmer P., Wei J., On the role of mean curvature in some singularly perturbed Neumann problems, SIAM J. Math. Anal. 31 (1999) 63-79. | MR | Zbl

[9] Del Pino M., Felmer P., Wei J., On the role of distance function in some singularly perturbed problems, Comm. PDE 25 (2000) 155-177. | MR | Zbl

[10] Del Pino M., Felmer P., Wei J., Mutiple peak solutions for some singular perturbation problems, Cal. Var. PDE 10 (2000) 119-134. | MR | Zbl

[11] Dancer E.N., Yan S., Multipeak solutions for a singular perturbed Neumann problem, Pacific J. Math. 189 (1999) 241-262. | MR | Zbl

[12] Dancer E.N., Yan S., Multi-layer solutions for an elliptic problem, J. Differential Equations 194 (2003) 382-405. | MR | Zbl

[13] Gui C., Wei J., Multiple interior spike solutions for some singular perturbed Neumann problems, J. Differential Equations 158 (1999) 1-27. | MR | Zbl

[14] Gui C., Wei J., On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems, Can. J. Math. 52 (2000) 522-538. | MR | Zbl

[15] Gui C., Wei J., Winter M., Multiple boundary peak solutions for some singularly perturbed Neumann problems, Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000) 249-289. | Numdam | MR | Zbl

[16] Grossi M., Pistoia A., Wei J., Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory, Cal. Var. PDE 11 (2000) 143-175. | MR | Zbl

[17] Li Y.-Y., On a singularly perturbed equation with Neumann boundary condition, Comm. PDE 23 (1998) 487-545. | MR | Zbl

[18] Li Y.-Y., Nirenberg L., The Dirichlet problem for singularly perturbed elliptic equations, Comm. Pure Appl. Math. 51 (1998) 1445-1490. | MR | Zbl

[19] Lin C.-S., Ni W.-M., Takagi I., Large amplitude stationary solutions to a chemotaxis systems, J. Differential Equations 72 (1988) 1-27. | MR | Zbl

[20] Malchiodi A., Montenegro M., Boundary concentration phenomena for a singularly perturbed elliptic problem, Comm. Pure Appl. Math. 55 (2002) 1507-1508. | MR | Zbl

[21] Nakashima K., Tanaka K., Clustering layers and boundary layers in spatially inhomogeneous phase transition problems, AIHP Analyse Nonlineaire 20 (1) (2003) 107-143. | Numdam | MR | Zbl

[22] Ni W.-M., Diffusion, cross-diffusion, and their spike-layer steady states, Notices Amer. Math. Soc. 45 (1998) 9-18. | MR | Zbl

[23] Ni W.-M., Takagi I., On the shape of least energy solution to a semilinear Neumann problem, Comm. Pure Appl. Math. 41 (1991) 819-851. | MR | Zbl

[24] Ni W.-M., Takagi I., Locating the peaks of least energy solutions to a semilinear Neumann problem, Duke Math. J. 70 (1993) 247-281. | MR | Zbl

[25] Ni W.-M., Takagi I., Point-condensation generated by a reaction-diffusion system in axially symmetric domains, Japan J. Industrial Appl. Math. 12 (1995) 327-365. | MR | Zbl

[26] Ni W.-M., Takagi I., Wei J., On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems: intermediate solutions, Duke Math. J. 94 (1998) 597-618. | MR | Zbl

[27] Ni W.-M., Wei J., On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Appl. Math. 48 (1995) 731-768. | MR | Zbl

[28] Wei J., On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem, J. Differential Equations 129 (1996) 315-333. | MR | Zbl

[29] Wei J., On the boundary spike layer solutions of singularly perturbed semilinear Neumann problem, J. Differential Equations 134 (1997) 104-133. | MR | Zbl

[30] Wei J., On the interior spike layer solutions to a singularly perturbed Neumann problem, Tohoku Math. J. 50 (1998) 159-178. | MR | Zbl

[31] Wei J., On the effect of the domain geometry in a singularly perturbed Dirichlet problem, Differential Integral Equations 13 (2000) 15-45. | MR | Zbl

[32] Wei J., Winter M., Stationary solutions for the Cahn-Hilliard equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998) 459-492. | Numdam | MR | Zbl

[33] Wei J., Winter M., Multiple boundary spike solutions for a wide class of singular perturbation problems, J. London Math. Soc. 59 (1999) 585-606. | MR | Zbl

Cité par Sources :