{
  "id": "0707.1952",
  "version": "v1",
  "published": "2007-07-13T09:47:03.000Z",
  "updated": "2007-07-13T09:47:03.000Z",
  "title": "Existence of positive solutions for nonlinear systems",
  "authors": [
    "Jifeng Chu",
    "Donal O'Regan",
    "Meirong Zhang"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper deals with the existence of positive solutions for the nonlinear system q(t)\\phi(p(t)u'_{i}(t)))'+f^{i}(t,\\textbf{u})=0,\\quad 0<t<1,\\quad i=1,2,...,n. This system often arises in the study of positive radial solutions of nonlinear elliptic system. Here $\\textbf{u}=(u_{1},...,u_{n})$ and $f^{i}, i=1,2,...,n$ are continuous and nonnegative functions, $p(t), q(t)\\hbox{\\rm :} [0,1]\\to (0,\\oo)$ are continuous functions. Moreover, we characterize the eigenvalue intervals for (q(t)\\phi(p(t)u'_{i}(t)))'+\\lambda h_{i}(t)g^{i} (\\textbf{u})=0, \\quad 0<t<1,\\quad i=1,2,...,n. The proof is based on a well-known fixed point theorem in cones.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-13T09:47:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34B15"
    ],
    "keywords": [
      "nonlinear system",
      "positive solutions",
      "nonlinear elliptic system",
      "well-known fixed point theorem",
      "paper deals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.1952C"
    }
  }
}