{
  "id": "1911.06038",
  "version": "v1",
  "published": "2019-11-14T11:05:56.000Z",
  "updated": "2019-11-14T11:05:56.000Z",
  "title": "Extremal constant sign solutions and nodal solutions for the fractional p-Laplacian",
  "authors": [
    "Silvia Frassu",
    "Antonio Iannizzotto"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a pseudo-differential equation driven by the degenerate fractional p-Laplacian, under Dirichlet type conditions in a smooth domain. First we show that the solution set within the order interval given by a sub-supersolution pair is nonempty, directed, and compact, hence endowed with extremal elements. Then, we prove existence of a smallest positive, a biggest negative and a nodal solution, combining variational methods with truncation techniques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-14T11:05:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A15",
      "35R11",
      "58E05"
    ],
    "keywords": [
      "extremal constant sign solutions",
      "nodal solution",
      "pseudo-differential equation driven",
      "degenerate fractional p-laplacian",
      "dirichlet type conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}