Multiplicity of multi-bump type nodal solutions for a class of elliptic problems with exponential critical growth in $\mathbb{R}^2$

Abstract

In this paper, we establish the existence and multiplicity of multi-bump nodal solutions for the following class of problems $$ -\Delta u+(\lambda V(x)+1)u=f(u),~~\mbox{in}~~\mathbb{R}^2, $$ where $\lambda\in(0,\infty)$, $f$ is a continuous function with exponential critical growth and $V:\mathbb{R}^2\to \mathbb{R}$ is a continuous function verifying some hypotheses.