Existence of multi-bump solutions to biharmonic operator with critical exponential growth in ${\mathbb{R}}^4$

Abstract

Using variational methods, we establish existence of multi-bump solutions for the following class of problems $$ \left\{ \begin{array}{l} Δ^2 u +(λV(x)+1)u = f(u), \quad \mbox{in} \quad \mathbb{R}^{4}, u \in H^{2}(\mathbb{R}^{4}), \end{array} \right. $$ where ${\Delta }^2$ is the biharmonic operator, $f$ is a continuous function with critical exponential growth and $V:{\mathbb{R}}^4\to \mathbb{R}$ is a continuous function verifying some conditions.

arXiv admin note: substantial text overlap with arXiv:1602.03112