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

Claudianor O. Alves

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.

Keywords


Variational methods; quasilinear problem; behaviour of solutions

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