American Institute of Mathematical Sciences

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2005, 2005(Special): 886-894. doi: 10.3934/proc.2005.2005.886

Stability and symmetry breaking of solutions of semilinear elliptic equations

Hwai-Chiuan Wang 1,

1. 

Department of Applied Mathematics, Hsuan Chuang University, Hsinchu, Taiwan

Received  July 2004 Revised  March 2005 Published  September 2005

In this article, we prove that there are three unstable positive solutions of a semilinear elliptic equation in a two bumps domain or in a one hole domain in which one is axially symmetric and the other two are nonaxially symmetric.
Keywords: stability, index of domain., symmetric breaking, semilinear elliptic equation, Palais- Smale sequence.
Mathematics Subject Classification: 35J20, 35J25, 35J6.
Citation: Hwai-Chiuan Wang. Stability and symmetry breaking of solutions of semilinear elliptic equations. Conference Publications, 2005, 2005 (Special) : 886-894. doi: 10.3934/proc.2005.2005.886
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