{
  "id": "0902.2507",
  "version": "v1",
  "published": "2009-02-15T00:59:37.000Z",
  "updated": "2009-02-15T00:59:37.000Z",
  "title": "Existence of weak solutions for nonlinear elliptic systems involving the (p(x), q(x))-Laplacian",
  "authors": [
    "Mounir Hsini"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we prove the existence of weak solutions for the following nonlinear elliptic system {lll} -\\Delta_{p(x)}u = a(x)|u|^{p(x)-2}u - b(x)|u|^{\\alpha(x)}|v|^{\\beta(x)} v + f(x) in \\Omega, \\Delta_{q(x)}v = c(x) |v|^{q(x)-2}v - d(x)|v|^{\\beta(x)}|u|^{\\alpha(x)} u + g(x) in \\Omega, u = v = 0 \\quad on \\partial\\Omega, where $\\Omega$ is an open bounded domains of $\\mathbb{R}^N$ with a smooth boundary $\\partial\\Omega$ and $\\Delta_{p(x)}$ denotes the $p(x)$-Laplacian.The existence of weak solutions is proved using the theory of monotone operators. Similar result will be proved when $\\Omega=\\mathbb{R}^N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-15T00:59:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B45",
      "35J55"
    ],
    "keywords": [
      "nonlinear elliptic system",
      "weak solutions",
      "open bounded domains",
      "smooth boundary",
      "monotone operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.2507H"
    }
  }
}