Multiplicity of multi-bump type nodal solutions for a class of elliptic problems in ${\mathbb R}^N$

Abstract

In this paper, we establish existence and multiplicity of multi-bump type nodal solutions for the following class of problems $$ -\Delta u + (\lambda V(x)+ 1)u= f(u), \quad u> 0 \quad \text{in } {\mathbb{R}}^N, $$ where $N \geq 1$, $\lambda \in (0, \infty)$, $f$ is a continuous function with subcritical growth and $V\colon {\mathbb{R}}^N \rightarrow \mathbb{R} $ is a continuous function verifying some hypotheses.