{
  "id": "1704.08001",
  "version": "v1",
  "published": "2017-04-26T07:58:52.000Z",
  "updated": "2017-04-26T07:58:52.000Z",
  "title": "Multiple solutions for resonant problems of the Robin $p$-Laplacian plus an indefinite potential",
  "authors": [
    "Nikolaos S. Papageorgiou",
    "Vicenţiu D. Rădulescu",
    "Dušan D. Repovš"
  ],
  "journal": "Calc. Var. 56:3 (2017)",
  "doi": "10.1007/s00526-017-1164-2",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a nonlinear boundary value problem driven by the $p$-Laplacian plus an indefinite potential with Robin boundary condition. The reaction term is a Carath\\'eodory function which is asymptotically resonant at $\\pm\\infty$ with respect to a nonprincipal Ljusternik-Schnirelmann eigenvalue. Using variational methods, together with Morse theory and truncation-perturbation techniques, we show that the problem has at least three nontrivial smooth solutions, two of which have a fixed sign.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-26T07:58:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35J60",
      "58E05"
    ],
    "keywords": [
      "indefinite potential",
      "laplacian plus",
      "resonant problems",
      "multiple solutions",
      "nonlinear boundary value problem driven"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}