{
  "id": "0901.0847",
  "version": "v1",
  "published": "2009-01-07T15:24:59.000Z",
  "updated": "2009-01-07T15:24:59.000Z",
  "title": "On positive solutions of p-Laplacian-type equations",
  "authors": [
    "Yehuda Pinchover",
    "Kyril Tintarev"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $\\Omega$ be a domain in $\\mathbb{R}^d$, $d\\geq 2$, and $1<p<\\infty$. Fix $V\\in L_{\\mathrm{loc}}^\\infty(\\Omega)$. Consider the functional $Q$ and its G\\^{a}teaux derivative $Q^\\prime$ given by $$Q(u):= \\frac{1}{p}\\int_\\Omega. (|\\nabla u|^p+V|u|^p) \\dx, Q^\\prime (u):= -\\nabla\\cdot(|\\nabla u|^{p-2}\\nabla u)+V|u|^{p-2} u.$$ In this paper we discuss a few aspects of relations between functional-analytic properties of the functional $Q$ and properties of positive solutions of the equation $Q^\\prime (u)=0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-07T15:24:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35J20",
      "35J70",
      "49R50"
    ],
    "keywords": [
      "positive solutions",
      "p-laplacian-type equations",
      "functional-analytic properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}