Existence of positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in $\mathbb{R}^{2}$

Claudianor O. Alves

Existence of positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in $\mathbb{R}^{2}$

Analysis of PDEs 2015-06-17 v1

Authors: Claudianor O. Alves

Abstract

In this paper, we use variational methods to prove the existence of positive solution for the following class of elliptic equation $-\epsilon^{2}\Delta{u}+V(z)u=f(u) \,\,\, \mbox{in} \,\,\, \mathbb{R}^{2},$ where $\epsilon >0$ is a positive parameter, $V$ is a saddle-like potential and $f$ has an exponential critical growth.

Keywords

nonlinear elliptic equation variational methods positive solution saddle-like potential exponential critical growth $\mathbb{R}^{2}$

Cite

@article{arxiv.1506.04947,
  title  = {Existence of positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in $\mathbb{R}^{2}$},
  author = {Claudianor O. Alves},
  journal= {arXiv preprint arXiv:1506.04947},
  year   = {2015}
}

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