On the existence and profile of multi-peaked solutions to singularly perturbed semilinear Dirichlet problems

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April 1996, 2(2): 221-236. doi: 10.3934/dcds.1996.2.221

On the existence and profile of multi-peaked solutions to singularly perturbed semilinear Dirichlet problems

Daomin Cao ^1, , Norman E. Dancer ^2, , Ezzat S. Noussair ^3, and Shunsen Yan ^4,

1.	Wuhan Institute of Mathematical Sciences, Wuhan, China
2.	University of Sydeny, NSW 2006, Australia
3.	School of Mathematics, The University of New South Wales, Sydney 2052, Australia
4.	South China University of Technology, Guangzhou 510641, China

Received February 1996 Published February 1996

Abstract
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Multi-peaked solutions to a singularly perturbed elliptic equation on a bounded domain $\Omega$ are constructed, provided the distance function $d(x, \delta\Omega)$ has more than one strict local maximum.

Keywords: semilinear Dirichlet problem., singular perturbation, multi-peaked solutions.

Mathematics Subject Classification: 35J20, 35J6.

Citation: Daomin Cao, Norman E. Dancer, Ezzat S. Noussair, Shunsen Yan. On the existence and profile of multi-peaked solutions to singularly perturbed semilinear Dirichlet problems. Discrete & Continuous Dynamical Systems - A, 1996, 2 (2) : 221-236. doi: 10.3934/dcds.1996.2.221

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