{
  "id": "math/0606157",
  "version": "v1",
  "published": "2006-06-07T14:37:07.000Z",
  "updated": "2006-06-07T14:37:07.000Z",
  "title": "Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: an Orlicz-Sobolev space setting",
  "authors": [
    "Mihai Mihailescu",
    "Vicentiu Radulescu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the boundary value problem $-{\\rm div}(\\log(1+ |\\nabla u|^q)|\\nabla u|^{p-2}\\nabla u)=f(u)$ in $\\Omega$, $u=0$ on $\\partial\\Omega$, where $\\Omega$ is a bounded domain in $\\RR^N$ with smooth boundary. We distinguish the cases where either $f(u)=-\\lambda|u|^{p-2}u+|u|^{r-2}u$ or $f(u)=\\lambda|u|^{p-2}u-|u|^{r-2}u$, with $p$, $q>1$, $p+q<\\min\\{N,r\\}$, and $r<(Np-N+p)/(N-p)$. In the first case we show the existence of infinitely many weak solutions for any $\\lambda>0$. In the second case we prove the existence of a nontrivial weak solution if $\\lambda$ is sufficiently large. Our approach relies on adequate variational methods in Orlicz-Sobolev spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-07T14:37:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D05",
      "35J60",
      "35J70",
      "46N20"
    ],
    "keywords": [
      "quasilinear nonhomogeneous problems",
      "orlicz-sobolev space setting",
      "multiplicity",
      "boundary value problem",
      "adequate variational methods"
    ],
    "publication": {
      "journal": "Journal of Mathematical Analysis and Applications",
      "year": 2007,
      "month": "Jun",
      "volume": 330,
      "number": 1,
      "pages": 416
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007JMAA..330..416M"
    }
  }
}