{
  "id": "2003.11863",
  "version": "v1",
  "published": "2020-03-26T12:30:57.000Z",
  "updated": "2020-03-26T12:30:57.000Z",
  "title": "Existence of solution for a class of nonlocal problem via dynamical methods",
  "authors": [
    "Claudianor O. Alves",
    "Tahir Boudjeriou"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we use the dynamical methods to establish the existence of nontrivial solution for a class of nonlocal problem of the type $$ \\left\\{\\begin{array}{l} -a\\left(x,\\int_{\\Omega}g(u)\\,dx \\right)\\Delta u =f(u), \\quad x \\in \\Omega \\\\ u=0, \\hspace{2 cm} x \\in \\partial \\Omega, \\end{array}\\right. \\leqno{(P)} $$ where $\\Omega \\subset \\mathbb{R}^N \\, ( N \\geq 2)$ is a smooth bounded domain and $a:\\overline{\\Omega} \\times \\mathbb{R} \\to \\mathbb{R}$ and $g,f: \\mathbb{R} \\to \\mathbb{R}$ are $C^1$-functions that satisfy some technical conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-26T12:30:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlocal problem",
      "dynamical methods",
      "nontrivial solution",
      "smooth bounded domain",
      "technical conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}