{
  "id": "1705.10111",
  "version": "v1",
  "published": "2017-05-29T10:50:25.000Z",
  "updated": "2017-05-29T10:50:25.000Z",
  "title": "Nonlinear problems on the Sierpiński gasket",
  "authors": [
    "Giovanni Molica Bisci",
    "Dušan D. Repovš",
    "Raffaella Servadei"
  ],
  "journal": "J. Math. Anal. Appl. {\\bf 452}:2 (2017), 883-895",
  "doi": "10.1016/j.jmaa.2017.03.032",
  "categories": [
    "math.AP",
    "math.OA",
    "math.OC"
  ],
  "abstract": "This paper concerns with a class of elliptic equations on fractal domains depending on a real parameter. Our approach is based on variational methods. More precisely, the existence of at least two non-trivial weak (strong) solutions for the treated problem is obtained exploiting a local minimum theorem for differentiable functionals defined on reflexive Banach spaces. A special case of the main result improves a classical application of the Mountain Pass Theorem in the fractal setting, given by Falconer and Hu (1999).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-29T10:50:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "35J20",
      "35J25",
      "35J60",
      "47J30",
      "49J52"
    ],
    "keywords": [
      "sierpiński gasket",
      "nonlinear problems",
      "local minimum theorem",
      "mountain pass theorem",
      "paper concerns"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}