{
  "id": "1602.04148",
  "version": "v1",
  "published": "2016-02-12T18:28:40.000Z",
  "updated": "2016-02-12T18:28:40.000Z",
  "title": "Multiple solutions for a Neumann system involving subquadratic nonlinearities",
  "authors": [
    "Alexandru Kristály",
    "Dušan Repovš"
  ],
  "journal": "Nonlinear Anal. 74:6 (2011), 2127-2132",
  "doi": "10.1016/j.na.2010.11.018",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we consider the model semilinear Neumann system $$\\left\\{ \\begin{array}{lll} -\\Delta u+a(x)u=\\lambda c(x) F_u(u,v)& {\\rm in} & \\Omega,\\\\ -\\Delta v+b(x)v=\\lambda c(x) F_v(u,v)& {\\rm in} & \\Omega,\\\\ \\frac{\\partial u}{\\partial \\nu}=\\frac{\\partial v}{\\partial \\nu}=0 & {\\rm on} & \\partial\\Omega, \\end{array}\\right.$$ where $\\Omega\\subset \\mathbb R^N$ is a smooth open bounded domain, $\\nu$ denotes the outward unit normal to $\\partial \\Omega$, $\\lambda\\geq 0$ is a parameter, $a,b,c\\in L_+^\\infty(\\Omega)\\setminus\\{0\\},$ and $F\\in C^1(\\mathbb{R}^2,\\mathbb{R})\\setminus\\{0\\}$ is a nonnegative function which is subquadratic at infinity. Two nearby numbers are determined in explicit forms, $\\underline \\lambda$ and $\\overline \\lambda$ with $ 0<\\underline\\lambda\\leq \\overline \\lambda$, such that for every $0\\leq \\lambda<\\underline \\lambda$, system $(N_\\lambda)$ has only the trivial pair of solution, while for every $\\lambda>\\overline \\lambda$, system $(N_\\lambda)$ has at least two distinct nonzero pairs of solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-12T18:28:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multiple solutions",
      "subquadratic nonlinearities",
      "model semilinear neumann system",
      "smooth open bounded domain",
      "distinct nonzero pairs"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160204148K"
    }
  }
}