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

Claudianor O. Alves; Denilson S. Pereira

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

Analysis of PDEs 2014-12-16 v1

Authors: Claudianor O. Alves , Denilson S. Pereira

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.

Keywords

elliptic problems nodal solutions multi-bump solutions exponential critical growth variational methods $\mathbb{R}^2$

Cite

@article{arxiv.1412.4219,
  title  = {Multiplicity of multi-bump type nodal solutions for a class of elliptic problems with exponential critical growth in $\mathbb{R}^2$},
  author = {Claudianor O. Alves and Denilson S. Pereira},
  journal= {arXiv preprint arXiv:1412.4219},
  year   = {2014}
}

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