{
  "id": "math/0606156",
  "version": "v1",
  "published": "2006-06-07T14:36:38.000Z",
  "updated": "2006-06-07T14:36:38.000Z",
  "title": "On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent",
  "authors": [
    "Mihai Mihailescu",
    "Vicentiu Radulescu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the nonlinear eigenvalue problem $-{\\rm div}(|\\nabla u|^{p(x)-2}\\nabla u)=\\lambda |u|^{q(x)-2}u$ in $\\Omega$, $u=0$ on $\\partial\\Omega$, where $\\Omega$ is a bounded open set in $\\RR^N$ with smooth boundary and $p$, $q$ are continuous functions on $\\bar\\Omega$ such that $1<\\inf\\_\\Omega q< \\inf\\_\\Omega p<\\sup\\_\\Omega q$, $\\sup\\_\\Omega p<N$, and $q(x)<Np(x)/(N-p(x))$ for all $x\\in\\bar\\Omega$. The main result of this paper establishes that any $\\lambda>0$ sufficiently small is an eigenvalue of the above nonhomogeneous quasilinear problem. The proof relies on simple variational arguments based on Ekeland's variational principle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-07T14:36:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D05",
      "35J60",
      "35J70",
      "58E05",
      "68T40",
      "76A02"
    ],
    "keywords": [
      "nonhomogeneous quasilinear eigenvalue problem",
      "sobolev spaces",
      "variable exponent",
      "nonlinear eigenvalue problem",
      "simple variational arguments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6156M"
    }
  }
}