{
  "id": "1508.04488",
  "version": "v1",
  "published": "2015-08-19T00:05:33.000Z",
  "updated": "2015-08-19T00:05:33.000Z",
  "title": "Existence of solutions for a nonlocal variational problem in $\\mathbb{R}^2$ with exponential critical growth",
  "authors": [
    "Claudianor O. Alves",
    "Minbo Yang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the existence of solution for the following class of nonlocal problem, $$ -\\Delta u +V(x)u =\\Big( I_\\mu\\ast F(x,u)\\Big)f(x,u) \\quad \\mbox{in} \\quad \\mathbb{R}^2, $$ where $V$ is a positive periodic potential, $I_\\mu=\\frac{1}{|x|^\\mu}$, $0<\\mu<2$ and $F(x,s)$ is the primitive function of $f(x,s)$ in the variable $s$. In this paper, by assuming that the nonlinearity $f(x,s)$ has an exponential critical growth at infinity, we prove the existence of solutions by using variational methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-19T00:05:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential critical growth",
      "nonlocal variational problem",
      "nonlocal problem",
      "positive periodic potential",
      "variational methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150804488A"
    }
  }
}