{
  "id": "2004.02776",
  "version": "v1",
  "published": "2020-04-06T16:07:43.000Z",
  "updated": "2020-04-06T16:07:43.000Z",
  "title": "Existence and multiplicity of positive solutions for the fractional Laplacian under subcritical or critical growth",
  "authors": [
    "Silvia Frassu",
    "Antonio Iannizzotto"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a Dirichlet type problem for an equation involving the fractional Laplacian and a reaction term subject to either subcritical or critical growth conditions, depending on a positive parameter. Applying a critical point result of Bonanno, we prove existence of one or two positive solutions as soon as the parameter lies under a (explicitly determined) threshold. As an application, we find two positive solutions for a fractional Brezis-Nirenberg problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-06T16:07:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R11",
      "35S15",
      "35A15"
    ],
    "keywords": [
      "positive solutions",
      "fractional laplacian",
      "critical growth",
      "multiplicity",
      "fractional brezis-nirenberg problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}