{
  "id": "1511.09406",
  "version": "v1",
  "published": "2015-11-30T17:45:06.000Z",
  "updated": "2015-11-30T17:45:06.000Z",
  "title": "Multiplicity results for the fractional laplacian in expanded domains",
  "authors": [
    "G. M. Figueiredo",
    "M. T. O Pimenta",
    "G. Siciliano"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we establish the multiplicity of nontrivial weak solutions for the problem $(-\\Delta)^{\\alpha} u +u= h(u)$ in $\\Omega_{\\lambda}$,\\ $u=0$ on $\\partial\\Omega_{\\lambda}$, where $\\Omega_{\\lambda}=\\lambda\\Omega$, $\\Omega$ is a smooth and bounded domain in $\\mathbb{R}^N, N>2\\alpha$, $\\lambda$ is a positive parameter, $\\alpha \\in (0,1)$, $(-\\Delta)^{\\alpha}$ is the fractional Laplacian and the nonlinear term $h(u)$ has a subcritical growth. We use minimax methods, the Ljusternick-Schnirelmann and Morse theories to get multiplicity result depending on the topology of $\\Omega$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-30T17:45:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiplicity result",
      "fractional laplacian",
      "expanded domains",
      "nontrivial weak solutions",
      "nonlinear term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151109406F"
    }
  }
}