{
  "id": "1506.04947",
  "version": "v1",
  "published": "2015-06-16T12:47:09.000Z",
  "updated": "2015-06-16T12:47:09.000Z",
  "title": "Existence of positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in $\\mathbb{R}^{2}$",
  "authors": [
    "Claudianor O. Alves"
  ],
  "categories": [
    "math.AP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-16T12:47:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential critical growth",
      "nonlinear elliptic equation",
      "positive solution",
      "saddle-like potential",
      "nonlinearity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150604947A"
    }
  }
}