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

Daomin Cao; Norman E. Dancer; Ezzat S. Noussair; Shunsen Yan

doi:10.3934/dcds.1996.2.221

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1996, Volume 2, Issue 2: 221-236. Doi: 10.3934/dcds.1996.2.221

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

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

Received: February 1996

Published: April 1996

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Abstract

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.

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Mathematics Subject Classification: 35J20, 35J65.

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

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