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Article Dans Une Revue Advances in Differential Equations Année : 2006

Multiple solutions to the supercritical Bahri-Coron's problem in pierced domains

Résumé

We consider the supercritical Dirichlet problem $$\left(P_\epsilon\right)\qquad -\Delta u=u^{{N+2\over N-2}+\epsilon}\ \hbox{in $\Omega$},\ u>0\ \hbox{in $\Omega,$}\ u=0\ \hbox{on $\partial\Omega$} $$ where $N\ge3,$ $\epsilon>0$ and $\Omega\subset\mathbb{R}^N$ is a smooth bounded domain with a small hole of radius $d.$ When $\Omega$ has some symmetries, we show that $\left(P_\epsilon\right)$ has an arbitrary number of solutions for $\epsilon$ and $d$ small enough. When $\Omega$ has no symmetries, we prove the existence, for $d$ small enough, of solutions blowing up at two or three points close to the hole as $\epsilon$ goes to zero.
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Dates et versions

hal-00935395 , version 1 (30-01-2014)

Identifiants

  • HAL Id : hal-00935395 , version 1

Citer

Angela Pistoia, Olivier Rey. Multiple solutions to the supercritical Bahri-Coron's problem in pierced domains. Advances in Differential Equations, 2006, 11 (6), pp.647-666. ⟨hal-00935395⟩
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