{
  "id": "0711.0904",
  "version": "v1",
  "published": "2007-11-06T15:37:59.000Z",
  "updated": "2007-11-06T15:37:59.000Z",
  "title": "A continuous spectrum for nonhomogeneous differential operators in Orlicz-Sobolev spaces",
  "authors": [
    "Mihai Mihailescu",
    "Vicentiu Radulescu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the nonlinear eigenvalue problem $-{\\rm div}(a(|\\nabla u|)\\nabla u)=\\lambda|u|^{q(x)-2}u$ in $\\Omega$, $u=0$ on $\\partial\\Omega$, where $\\Omega$ is a bounded open set in $\\RR^N$ with smooth boundary, $q$ is a continuous function, and $a$ is a nonhomogeneous potential. We establish sufficient conditions on $a$ and $q$ such that the above nonhomogeneous quasilinear problem has continuous families of eigenvalues. The proofs rely on elementary variational arguments. The abstract results of this paper are illustrated by the cases $a(t)=t^{p-2}\\log (1+t^r)$ and $a(t)= t^{p-2} [\\log (1+t)]^{-1}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-06T15:37:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D05",
      "35J60",
      "35J70",
      "58E05",
      "68T40",
      "76A02"
    ],
    "keywords": [
      "nonhomogeneous differential operators",
      "orlicz-sobolev spaces",
      "continuous spectrum",
      "nonlinear eigenvalue problem",
      "elementary variational arguments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.0904M"
    }
  }
}