### 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.

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.

#### Keywords

Variational methods; quasilinear problem; behaviour of solutions

#### Full Text:

FULL TEXT### Refbacks

- There are currently no refbacks.