{
  "id": "1604.00808",
  "version": "v1",
  "published": "2016-04-04T10:52:32.000Z",
  "updated": "2016-04-04T10:52:32.000Z",
  "title": "Existence and multiplicity of solutions for a class of quasilinear problems in Orlicz-Sobolev spaces",
  "authors": [
    "Karima Ait-Mahiout",
    "Claudianor O. Alves"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This work is concerned with the existence and multiplicity of solutions for the following class of quasilinear problems $$ -\\Delta_{\\Phi}u+\\phi(|u|)u=f(u)~\\text{in} ~\\Omega_{\\lambda}, u(x)>0 ~\\text{in}~\\Omega_{\\lambda}, u=0~ \\mbox{on} ~\\partial\\Omega_{\\lambda}, $$ where $\\Phi(t)=\\int_0^{|t|} \\phi(s) s \\, ds $ is an $N-$function, $\\Delta_{\\Phi}$ is the $\\Phi-$Laplacian operator, \\linebreak $\\Omega_{\\lambda}=\\lambda \\Omega,$ $\\Omega$ is a smooth bounded domain in $\\mathbb{R}^N,$ $N \\geq 2$, $\\lambda$ is a positive parameter and $f: \\mathbb{R}\\rightarrow \\mathbb{R}$ is a continuous function. Here, we use variational methods to get multiplicity of solutions by using of Lusternik-Schnirelmann category of ${\\Omega}$ in itself.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-04T10:52:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasilinear problems",
      "orlicz-sobolev spaces",
      "multiplicity",
      "laplacian operator",
      "smooth bounded domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160400808A"
    }
  }
}