Multiple solutions for the p-laplace operator with critical growth

PABLO DE NÁPOLI,JULIAN FERNÁNDEZ BONDER, ANALÍA SILVA

JOURNAL OF NONLINEAR ANALYSIS

PERGAMON-ELSEVIER SCIENCE LTD

Año: 2009 vol. 71 p. 6283 - 6289

0362-546X

In this paper 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 $partialOmega$, where $p^*=Np/(N-p)$ is the critical Sobolev exponent and $Delta_p u = mbox{div}(| abla u|^{p-2} abla u)$ is the $p-$laplacian. The proof is based on variational arguments and the classical concentration compactness method.