%0 Journal Article
%T Multiple solutions for the $p-$laplace operator with critical growth
%A Pablo L. De N¨˘poli
%A Juli¨˘n Fern¨˘ndez Bonder
%A Anal¨Şa Silva
%J Mathematics
%D 2008
%I arXiv
%R 10.1016/j.na.2009.06.036
%X 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.
%U http://arxiv.org/abs/0808.3143v2