{
  "id": "1709.05497",
  "version": "v1",
  "published": "2017-09-16T11:15:33.000Z",
  "updated": "2017-09-16T11:15:33.000Z",
  "title": "Non-existence of stable solutions for weighted $p$-Laplace equation",
  "authors": [
    "Kaushik Bal",
    "Prashanta Garain"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We provide sufficient conditions on $w\\in L^1_{loc}(\\mathbb{R}^N)$ such that the weighted $p$-Laplace equation $$-\\operatorname{div}\\big(w(x)|\\nabla u|^{p-2}\\nabla u\\big)=f(u)\\;\\;\\mbox{in}\\;\\;\\mathbb{R}^N$$ does not admit any stable $C^{1,\\zeta}_{loc}$ solution in $\\mathbb{R}^N$ where $f(x)$ is either $-x^{-\\delta}$ or $e^x$ for any $0<\\zeta<1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-16T11:15:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35B93",
      "35J92"
    ],
    "keywords": [
      "laplace equation",
      "stable solutions",
      "non-existence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}