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 \[ - \mbox{div}\big(ε^{2}ϕ(ε|\nabla u|)\nabla u\big) + V(x)ϕ(| u|)u = f(u)\quad \mbox{in} \quad \mathbb{R}^{N}, \] where $\epsilon$ is a positive parameter, $N\ge 2$, $V,f$ are continuous functions satisfying some technical conditions and $\varphi$ is a $C^1$-function.