{
  "id": "1310.5636",
  "version": "v1",
  "published": "2013-10-21T16:42:46.000Z",
  "updated": "2013-10-21T16:42:46.000Z",
  "title": "On the Structure of the Solution Set of a Sign Changing Perturbation of the p-Laplacian under Dirichlet Boundary Condition",
  "authors": [
    "J. V. Goncalves",
    "M. R. Marcial"
  ],
  "comment": "23 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In a recent paper D. D. Hai showed that the equation $ -\\Delta_{p} u = \\lambda f(u) \\mbox{in} \\Omega$, under Dirichlet boundary condition, where $\\Omega \\subset {\\bf R^N}$ is a bounded domain with smooth boundary $\\partial\\Omega$, $\\Delta_{p}$ is the p-Laplacian, $f : (0,\\infty) \\rightarrow {\\bf R} $ is a continuous function which may blow up to $\\pm \\infty$ at the origin, admits a solution if $\\lambda > \\lambda_0$ and has no solution if $0 < \\lambda < \\lambda_0$. In this paper we show that the solution set $\\mathcal{S}$ of the equation above, which is not empty by Hai's results, actually admits a continuum of positive solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-21T16:42:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J25",
      "35J55",
      "35J70"
    ],
    "keywords": [
      "dirichlet boundary condition",
      "sign changing perturbation",
      "solution set",
      "p-laplacian",
      "hais results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.5636G"
    }
  }
}