Multiple solutions for the $p-$laplace operator with critical growth

Date
Authors
De Nápoli, Pablo L.
Bonder, Julián Fernández
Silva, Analía
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
In this note we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation $-\Delta_p u = |u|^{p^*-2}u + \lambda f(x,u)$ in a smooth bounded domain $\Omega$ of $\R^N$ with homogeneous Dirichlet boundary conditions on $\partial\Omega$, where $p^*=Np/(N-p)$ is the critical Sobolev exponent and $\Delta_p u =div(|\nabla u|^{p-2}\nabla u)$ is the $p-$laplacian. The proof is based on variational arguments and the classical concentrated compactness method.
Comment: Results improved, hypotheses removed
Keywords
Mathematics - Analysis of PDEs, 35J60, 35J20
Citation
Collections