Multiplicity of solutions for a quasilinear problem with supercritical growth

Abstract

The multiplicity and concentration of positive solutions are established for the equation $$ -epsilon^{p}Delta_{p}u+V(z)|u|^{p-2}u=|u|^{q-2}u +lambda|u|^{s-2}u quadhbox{in }mathbb{R}^N, $$ where $10$, $p<q<p^* leq s$, $p^{*}=frac{Np}{N-p}$, $lambdageq 0$ and $V$ is a positive continuous function.

Keywords

• Variational method
• penalization method
• Moser iteration method.