{
  "id": "1703.04229",
  "version": "v1",
  "published": "2017-03-13T02:48:38.000Z",
  "updated": "2017-03-13T02:48:38.000Z",
  "title": "An indefinite concave-convex equation under a Neumann boundary condition II",
  "authors": [
    "Humberto Ramos Quoirin",
    "Kenichiro Umezu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We proceed with the investigation of the problem $(P_\\lambda): $ $-\\Delta u = \\lambda b(x)|u|^{q-2}u +a(x)|u|^{p-2}u \\ \\mbox{ in } \\Omega, \\ \\ \\frac{\\partial u}{\\partial \\mathbf{n}} = 0 \\ \\mbox{ on } \\partial \\Omega$, where $\\Omega$ is a bounded smooth domain in $\\mathbb{R}^N$ ($N \\geq2$), $1<q<2<p$, $\\lambda \\in \\mathbb{R}$, and $a,b \\in C^\\alpha(\\overline{\\Omega})$ with $0<\\alpha<1$. Dealing now with the case $b \\geq 0$, $b \\not \\equiv 0$, we show the existence (and several properties) of a unbounded subcontinuum of nontrivial non-negative solutions of $(P_\\lambda)$. Our approach is based on a priori bounds, a regularization procedure, and Whyburn's topological method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-13T02:48:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "neumann boundary condition",
      "indefinite concave-convex equation",
      "bounded smooth domain",
      "nontrivial non-negative solutions",
      "priori bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}