{
  "id": "1211.5769",
  "version": "v1",
  "published": "2012-11-25T15:51:06.000Z",
  "updated": "2012-11-25T15:51:06.000Z",
  "title": "Positive and sign changing solutions to a nonlinear Choquard equation",
  "authors": [
    "Mónica Clapp",
    "Dora Salazar"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the problem \\[-\\Delta u + W(x)u = ((1/{|x|^{\\alpha}} * |u|^{p}) |u|^{p-2}u, u \\in H_{0}^{1}(\\Omega)\\], where $\\Omega$ is an exterior domain in $\\mathbb{R}^{N}$, $N\\geq3,$ $\\alpha \\in(0,N)$, $p\\in[2,(2N-\\alpha)/(N-2)$, $W$ is continuous, $\\inf_{\\mathbb{R}^{N}}W>0,$ and $W(x)$ tends to a positive constant as $|x|$ tends to infinity. Under symmetry assumptions on $\\Omega$ and $W$, which allow finite symmetries, and some assumptions on the decay of $W$ at infinity, we establish the existence of a positive solution and multiple sign changing solutions to this problem, having small energy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-25T15:51:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J91",
      "35A01",
      "35B06",
      "35J20",
      "35Q55"
    ],
    "keywords": [
      "nonlinear choquard equation",
      "multiple sign changing solutions",
      "symmetry assumptions",
      "finite symmetries",
      "small energy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.5769C"
    }
  }
}