{
  "id": "1912.12205",
  "version": "v1",
  "published": "2019-12-24T10:00:03.000Z",
  "updated": "2019-12-24T10:00:03.000Z",
  "title": "Pairs of positive radial solutions for a Minkowski-curvature Neumann problem with indefinite weight",
  "authors": [
    "Alberto Boscaggin",
    "Guglielmo Feltrin"
  ],
  "comment": "17 pages, 4 PDF figures",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "We prove the existence of a pair of positive radial solutions for the Neumann boundary value problem \\begin{equation*} \\begin{cases} \\, \\mathrm{div}\\,\\Biggl{(} \\dfrac{\\nabla u}{\\sqrt{1- | \\nabla u |^{2}}}\\Biggr{)} + \\lambda a(|x|)u^p = 0, & \\text{in $B$,} \\\\ \\, \\partial_{\\nu}u=0, & \\text{on $\\partial B$,} \\end{cases} \\end{equation*} where $B$ is a ball centered at the origin, $a(|x|)$ is a radial sign-changing function with $\\int_B a(|x|)\\,\\mathrm{d}x < 0$, $p>1$ and $\\lambda > 0$ is a large parameter. The proof is based on the Leray-Schauder degree theory and extends to a larger class of nonlinearities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-24T10:00:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34B08",
      "34B18",
      "35B09",
      "47H11"
    ],
    "keywords": [
      "positive radial solutions",
      "minkowski-curvature neumann problem",
      "indefinite weight",
      "neumann boundary value problem",
      "leray-schauder degree theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}