The existence of three solutions for $p$-Laplacian problems with critical and supercritical growth

Abstract

In this paper we deal with the existence and multiplicity of solutions for the $p$-Laplacian problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation combining with the Moser iteration, we extend the result obtained by Ricceri \cite{14} to the critical and supercritical case.