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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

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 and Continuous Dynamical Systems, 1996, 2 (2) : 221-236. doi: 10.3934/dcds.1996.2.221
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