Existence of Multi-peak Solutions for a Class of Quasilinear Problems in Orlicz-Sobolev Spaces

Abstract

The aim of this work is to establish the existence of multi-peak solutions for the following class of quasilinear problems $$ - \mbox{div} \bigl(\epsilon^{2}\phi\bigl(\epsilon|\nabla u|\bigr)\nabla u \bigr) + V(x)\phi\bigl(\vert u\vert\bigr)u = f(u)\quad\mbox{in } \mathbb{R}^{N}, $$ where $\epsilon$ is a positive parameter, $N\geq2$ , $V$ , $f$ are continuous functions satisfying some technical conditions and $\phi$ is a $C^{1}$ -function.