{
  "id": "0904.1489",
  "version": "v1",
  "published": "2009-04-09T09:42:38.000Z",
  "updated": "2009-04-09T09:42:38.000Z",
  "title": "On the positive solutions to some quasilinear elliptic partial differential equations",
  "authors": [
    "Octavian G. Mustafa",
    "Yong Zhou"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We establish that the elliptic equation $\\Delta u+f(x,u)+g(| x|)x\\cdot \\nabla u=0$, where $x\\in\\mathbb{R}^{n}$, $n\\geq3$, and $| x|>R>0$, has a positive solution which decays to 0 as $| x|\\to +\\infty$ under mild restrictions on the functions $f,g$. The main theorem extends and complements the conclusions of the recent paper [M. Ehrnstr\\\"{o}m, O.G. Mustafa, On positive solutions of a class of nonlinear elliptic equations, Nonlinear Anal. TMA 67 (2007), 1147--1154]. Its proof relies on a general result about the long-time behavior of the logarithmic derivatives of solutions for a class of nonlinear ordinary differential equations and on the comparison method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-09T09:42:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A35",
      "35B40"
    ],
    "keywords": [
      "quasilinear elliptic partial differential equations",
      "positive solution",
      "nonlinear ordinary differential equations",
      "nonlinear elliptic equations",
      "main theorem extends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.1489M"
    }
  }
}