{
  "id": "1610.09328",
  "version": "v1",
  "published": "2016-10-28T17:54:46.000Z",
  "updated": "2016-10-28T17:54:46.000Z",
  "title": "Positive solutions for the fractional Laplacian in the almost critical case in a bounded domain",
  "authors": [
    "G. M. Figueiredo",
    "G. Siciliano"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:0905.2358",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove existence of multiple positive solutions for a {\\sl fractional scalar field equation} in a bounded domain, whenever $p$ tends to the critical Sobolev exponent. By means of the \"photography method\", we prove that the topology of the domain furnishes a lower bound on the number of positive solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-28T17:54:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded domain",
      "fractional laplacian",
      "critical case",
      "fractional scalar field equation",
      "multiple positive solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}