Multiple solutions for a non-homogeneous elliptic equation at the critical exponent

Mónica Clapp; Manuel Del Pino; Monica Musso

doi:10.1017/S0308210500003085

Abstract

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We consider the equation−Δu = |u|4/(N−2)u + εf(x) under zero Dirichlet boundary conditions in a bounded domain Ω in RN exhibiting certain symmetries, with f ≥ 0, f ≠ 0. In particular, we find that the number of sign-changing solutions goes to infinity for radially symmetric f, as ε → 0 if Ω is a ball. The same is true for the number of negative solutions if Ω is an annulus and the support of f is compact in Ω.

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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Multiple solutions for a non-homogeneous elliptic equation at the critical exponent

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