{
  "id": "1702.05287",
  "version": "v1",
  "published": "2017-02-17T10:15:43.000Z",
  "updated": "2017-02-17T10:15:43.000Z",
  "title": "A strongly indefinite Choquard equation with critical exponent due to the Hardy-Littlewood-Sobolev inequality",
  "authors": [
    "Fashun Gao",
    "Minbo Yang"
  ],
  "comment": "17pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we are concerned with the following nonlinear Choquard equation $$-\\Delta u+V(x)u =\\left(\\int_{\\mathbb{R}^N}\\frac{G(y,u)}{|x-y|^{\\mu}}dy\\right)g(x,u)\\hspace{4.14mm}\\mbox{in}\\hspace{1.14mm} \\mathbb{R}^N, $$ where $N\\geq4$, $0<\\mu<N$ and $G(x,u)=\\displaystyle\\int^u_0g(x,s)ds$. If $0$ lies in a gap of the spectrum of $-\\Delta +V$ and $g(x,u)$ is of critical growth due to the Hardy-Littlewood-Sobolev inequality, we obtain the existence of nontrivial solutions by variational methods. The main result here extends and complements the earlier theorems obtained in \\cite{AC, KS, MS2}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-17T10:15:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35J60",
      "35J20",
      "35J60",
      "35J20"
    ],
    "keywords": [
      "strongly indefinite choquard equation",
      "hardy-littlewood-sobolev inequality",
      "critical exponent",
      "nonlinear choquard equation",
      "nontrivial solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}