{
  "id": "1707.07079",
  "version": "v1",
  "published": "2017-07-22T00:29:29.000Z",
  "updated": "2017-07-22T00:29:29.000Z",
  "title": "Existence and nonexistence of positive solutions to some fully nonlinear equation in one dimension",
  "authors": [
    "Patricio Felmer",
    "Norihisa Ikoma"
  ],
  "comment": "29 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the existence (and nonexistence) of solutions to \\[ -\\mathcal{M}_{\\lambda,\\Lambda}^\\pm (u'') + V(x) u = f(u) \\quad {\\rm in} \\ \\mathbf{R} \\] where $\\mathcal{M}_{\\lambda,\\Lambda}^+$ and $\\mathcal{M}_{\\lambda,\\Lambda}^-$ denote the Pucci operators with $0< \\lambda \\leq \\Lambda < \\infty$, $V(x)$ is a bounded function, $f(s)$ is a continuous function and its typical example is a power-type nonlinearity $f(s) =|s|^{p-1}s$ $(p>1)$. In particular, we are interested in positive solutions which decay at infinity, and the existence (and nonexistence) of such solutions is proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-22T00:29:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fully nonlinear equation",
      "positive solutions",
      "nonexistence",
      "pucci operators",
      "power-type nonlinearity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}