{
  "id": "1408.1806",
  "version": "v2",
  "published": "2014-08-08T10:21:05.000Z",
  "updated": "2016-02-18T07:53:00.000Z",
  "title": "Liouville Type Theorem For A Nonlinear Neumann Problem",
  "authors": [
    "Changlin Xiang"
  ],
  "comment": "This paper has been withdrawn by the author due to a poor writing",
  "categories": [
    "math.AP"
  ],
  "abstract": "Consider the following nonlinear Neumann problem \\[ \\begin{cases} \\text{div}\\left(y^{a}\\nabla u(x,y)\\right)=0, & \\text{for }(x,y)\\in\\mathbb{R}_{+}^{n+1}\\\\ \\lim_{y\\rightarrow0+}y^{a}\\frac{\\partial u}{\\partial y}=-f(u), & \\text{on }\\partial\\mathbb{R}_{+}^{n+1},\\\\ u\\ge0 & \\text{in }\\mathbb{R}_{+}^{n+1}, \\end{cases} \\] $a\\in(-1,1)$. A Liouville type theorem and its applications are given under suitable conditions on $f$. Our tool is the famous moving plane method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-08T10:21:05.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-02-18T07:53:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35J25",
      "35J65"
    ],
    "keywords": [
      "liouville type theorem",
      "nonlinear neumann problem",
      "famous moving plane method",
      "suitable conditions",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.1806X"
    }
  }
}