{
  "id": "1605.05038",
  "version": "v1",
  "published": "2016-05-17T07:08:09.000Z",
  "updated": "2016-05-17T07:08:09.000Z",
  "title": "Existence and multiplicity of solutions for a class of Choquard equations with Hardy-Littlewood-Sobolev critical exponent",
  "authors": [
    "Fashun Gao",
    "Minbo Yang"
  ],
  "comment": "30",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the following nonlinear Choquard equation with Dirichlet boundary condition $$-\\Delta u =\\left(\\int_{\\Omega}\\frac{|u|^{2_{\\mu}^{\\ast}}}{|x-y|^{\\mu}}dy\\right)|u|^{2_{\\mu}^{\\ast}-2}u+\\lambda f(u)\\hspace{4.14mm}\\mbox{in}\\hspace{1.14mm} \\Omega, $$ where $\\Omega$ is a smooth bounded domain of $\\mathbb{R}^N$, $\\lambda>0$, $N\\geq3$, $0<\\mu<N$ and $2_{\\mu}^{\\ast}$ is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality. Under suitable assumptions on different types of nonlinearities $f(u)$, we are able to prove some existence and multiplicity results for the equation by variational methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-17T07:08:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J25",
      "35J25"
    ],
    "keywords": [
      "hardy-littlewood-sobolev critical exponent",
      "nonlinear choquard equation",
      "dirichlet boundary condition",
      "smooth bounded domain",
      "hardy-littlewood-sobolev inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}