{
  "id": "0707.2169",
  "version": "v1",
  "published": "2007-07-14T21:03:51.000Z",
  "updated": "2007-07-14T21:03:51.000Z",
  "title": "On positive solutions of minimal growth for singular p-Laplacian with potential term",
  "authors": [
    "Yehuda Pinchover",
    "Kyril Tintarev"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AP",
    "math.SP"
  ],
  "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. It is assumed that $Q\\geq 0$ on $C_0^\\infty(\\Omega)$. In a previous paper we discussed relations between the absence of weak coercivity of the functional $Q$ on $C_0^\\infty(\\Omega)$ and the existence of a generalized ground state. In the present paper we study further relationships between functional-analytic properties of the functional $Q$ and properties of positive solutions of the equation $Q^\\prime (u)=0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-14T21:03:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35J60",
      "35J70",
      "49R50"
    ],
    "keywords": [
      "positive solutions",
      "potential term",
      "minimal growth",
      "singular p-laplacian",
      "weak coercivity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.2169P"
    }
  }
}