Multiple solutions for the p-laplace operator with critical growth

2008/08/31 by Pablo L. De Nápoli, Julián Fernández Bonder, Analía Silva · 1 citation
Mathematics · #math.AP #msc:35J20 #msc:35J60

paper · pdf · doi:10.1016/j.na.2009.06.036

published as Nonlinear Anal. TMA., 71 (2009), 6283--6289. · Results improved, hypotheses removed

arxiv created 2009/02/25 · arxiv updated 2010/03/15

Abstract

In this note we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation -Δ_p u = |u|^{p^*-2}u + λf(x,u) in a smooth bounded domain Ω of \R^N with homogeneous Dirichlet boundary conditions on ∂Ω, where p^*=Np/(N-p) is the critical Sobolev exponent and Δ_p u =div(|∇ u|^p-2∇ u) is the p-laplacian. The proof is based on variational arguments and the classical concentrated compactness method.

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