Existence of multi-peak solutions for a class of quasilinear problems in Orlicz-Sobolev spaces

摘要

The aim of this work is to establish the existence of multi-peak solutionsfor the following class of quasilinear problems \[ -\mbox{div}\big(\epsilon^{2}\phi(\epsilon|\nabla u|)\nabla u\big) + V(x)\phi(|u|)u = f(u)\quad \mbox{in} \quad \mathbb{R}^{N}, \] where $\epsilon$ is apositive parameter, $ N\geq 2$, $V, f$ are continuous functions satisfying sometechnical conditions and $\phi$ is a $C^{1}$-function.