{
  "id": "1607.04510",
  "version": "v1",
  "published": "2016-07-15T13:56:51.000Z",
  "updated": "2016-07-15T13:56:51.000Z",
  "title": "Existence of positive solution for a system of elliptic equations via bifurcation theory",
  "authors": [
    "Romildo N. de Lima",
    "Marco A. S. Souto"
  ],
  "comment": "21 pages. arXiv admin note: text overlap with arXiv:1509.05294",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study the existence of solution for the following class of system of elliptic equations $$ \\left\\{ \\begin{array}{lcl} -\\Delta u=\\left(a-\\int_{\\Omega}K(x,y)f(u,v)dy\\right)u+bv,\\quad \\mbox{in} \\quad \\Omega -\\Delta v=\\left(d-\\int_{\\Omega}\\Gamma(x,y)g(u,v)dy\\right)v+cu,\\quad \\mbox{in} \\quad \\Omega u=v=0,\\quad \\mbox{on} \\quad \\partial\\Omega \\end{array} \\right. \\eqno{(P)} $$ where $\\Omega\\subset\\R^N$ is a smooth bounded domain, $N\\geq1$, and $K,\\Gamma:\\Omega\\times\\Omega\\rightarrow\\R$ is a nonnegative function checking some hypotheses and $a,b,c,d\\in\\R$. The functions $f$ and $g$ satisfy some conditions which permit to use Bifurcation Theory to prove the existence of solution for $(P)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-15T13:56:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic equations",
      "bifurcation theory",
      "positive solution",
      "smooth bounded domain",
      "nonnegative function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}