Existence of multi-bump solutions for a class of elliptic problems involving the biharmonic operator

Abstract

Using variational methods, we establish existence of multi-bump solutions for the following class of problems $$ \left\{ \begin{array}{l} Δ^2 u +(λV(x)+1)u = f(u), \quad \mbox{in} \quad \mathbb{R}^{N}, u \in H^{2}(\mathbb{R}^{N}), \end{array} \right. $$ where $N\ge 1$, ${\Delta }^2$ is the biharmonic operator, $f$ is a continuous function with subcritical growth and $V:{\mathbb{R}}^N\to \mathbb{R}$ is a continuous function verifying some conditions.

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