{
  "id": "1704.03562",
  "version": "v1",
  "published": "2017-04-11T22:52:02.000Z",
  "updated": "2017-04-11T22:52:02.000Z",
  "title": "Existence of solution for a class of quasilinear problem in Orlicz-Sobolev space without $Δ_2$-condition",
  "authors": [
    "Claudianor O. Alves",
    "Edcarlos D. Silva",
    "Marcos T. O. Pimenta"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "\\noindent In this paper we study existence of solution for a class of problem of the type $$ \\left\\{ \\begin{array}{ll} -\\Delta_{\\Phi}{u}=f(u), \\quad \\mbox{in} \\quad \\Omega u=0, \\quad \\mbox{on} \\quad \\partial \\Omega, \\end{array} \\right. $$ where $\\Omega \\subset \\mathbb{R}^N$, $N \\geq 2$, is a smooth bounded domain, $f:\\mathbb{R} \\to \\mathbb{R}$ is a continuous function verifying some conditions, and $\\Phi:\\mathbb{R} \\to \\mathbb{R}$ is a N-function which is not assumed to satisfy the well known $\\Delta_2$-condition, then the Orlicz-Sobolev space $W^{1,\\Phi}_0(\\Omega)$ can be non reflexive. As main model we have the function $\\Phi(t)=(e^{t^{2}}-1)/2$. Here, we study some situations where it is possible to work with global minimization, local minimization and mountain pass theorem, however some estimates are not standard for this type of problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-11T22:52:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "orlicz-sobolev space",
      "quasilinear problem",
      "mountain pass theorem",
      "smooth bounded domain",
      "main model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}