{
  "id": "1309.1109",
  "version": "v1",
  "published": "2013-09-04T17:17:00.000Z",
  "updated": "2013-09-04T17:17:00.000Z",
  "title": "Qualitative properties of a nonlinear system involving the $p$-Laplacian operator",
  "authors": [
    "Françoise Demengel"
  ],
  "comment": "29 pages, no figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article we consider the nonlinear system involving the $p$-Laplacian $$\\left\\{\\begin{array}{lc} |u^\\prime |^{p-2} u^{\\prime \\prime} = u^{p-1} v^p& |v^\\prime |^{p-2} v^{\\prime \\prime} = v^{p-1} u^p&\\ {\\rm on} \\ \\R, u\\geq 0, v\\geq 0& \\end{array}\\right.$$ for which we prove symmetry, asymptotic behavior and non degeneracy properties. This can help to a better understanding to what happens in the $N$ dimensional case, for which several authors prove a De Giorgi Type result under some additional growth and monotonicity assumptions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-04T17:17:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "B50"
    ],
    "keywords": [
      "nonlinear system",
      "laplacian operator",
      "qualitative properties",
      "non degeneracy properties",
      "giorgi type result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.1109D"
    }
  }
}