{
  "id": "0905.2358",
  "version": "v2",
  "published": "2009-05-14T15:48:00.000Z",
  "updated": "2009-06-22T09:21:06.000Z",
  "title": "Multiple positive solutions for a Schrödinger-Poisson-Slater system",
  "authors": [
    "Gaetano Siciliano"
  ],
  "comment": "added references and improved the result",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we investigate the existence of positive solutions to the following Schr\\\"odinger-Poisson-Slater system [c]{ll} - \\Delta u+ u + \\lambda\\phi u=|u|^{p-2}u & \\text{in} \\Omega -\\Delta\\phi= u^{2} & \\text{in} \\Omega u=\\phi=0 & \\text{on} \\partial\\Omega. where $\\Omega$ is a bounded domain in $\\mathbf{R}^{3},\\lambda$ is a fixed positive parameter and $p<2^{*}=\\frac{2N}{N-2}$. We prove that if $p$ is \"near\" the critical Sobolev exponent $2^*$, then the number of positive solutions is greater then the Ljusternik-Schnirelmann category of $\\Omega$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-06-22T09:21:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J50",
      "55M30",
      "74G35"
    ],
    "keywords": [
      "multiple positive solutions",
      "schrödinger-poisson-slater system",
      "critical sobolev exponent",
      "ljusternik-schnirelmann category",
      "bounded domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.2358S"
    }
  }
}