Existence of multi-peak solutions for a class of quasilinear problems in $\mathbb{R}^{N}$

Abstract

Using variational methods we establish existence of multi-peak solutions for the following class of quasilinear problems $$ -\varepsilon^{p}\Delta_{p}u + V(x)u^{p-1}= f(u), \quad u> 0, \text{ in } {\mathbb{R}}^{N} $$ where $\Delta_{p}u$ is the $p$-Laplacian operator, $2 \leq p < N$, $\varepsilon > 0$ and $f$ is a continuous function with subcritical growth.