{
  "id": "0808.3143",
  "version": "v2",
  "published": "2008-08-22T20:27:01.000Z",
  "updated": "2009-02-25T14:11:37.000Z",
  "title": "Multiple solutions for the $p-$laplace operator with critical growth",
  "authors": [
    "Pablo L. De Nápoli",
    "Julián Fernández Bonder",
    "Analía Silva"
  ],
  "comment": "Results improved, hypotheses removed",
  "journal": "Nonlinear Anal. TMA., 71 (2009), 6283--6289.",
  "doi": "10.1016/j.na.2009.06.036",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this note we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation $-\\Delta_p u = |u|^{p^*-2}u + \\lambda f(x,u)$ in a smooth bounded domain $\\Omega$ of $\\R^N$ with homogeneous Dirichlet boundary conditions on $\\partial\\Omega$, where $p^*=Np/(N-p)$ is the critical Sobolev exponent and $\\Delta_p u =div(|\\nabla u|^{p-2}\\nabla u)$ is the $p-$laplacian. The proof is based on variational arguments and the classical concentrated compactness method.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-02-25T14:11:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35J20"
    ],
    "keywords": [
      "multiple solutions",
      "laplace operator",
      "critical growth",
      "quasilinear elliptic equation",
      "homogeneous dirichlet boundary conditions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.3143D"
    }
  }
}