{
  "id": "1311.2204",
  "version": "v2",
  "published": "2013-11-09T20:18:59.000Z",
  "updated": "2013-12-19T20:52:44.000Z",
  "title": "Ground state solution of a nonlocal boundary-value problem",
  "authors": [
    "Cyril Joel Batkam"
  ],
  "comment": "8 pages",
  "journal": "Electron. J. Diff. Equ., Vol. 2013 (2013), No. 257, pp. 1-8",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we apply the method of the Nehari manifold to study the Kirchhoff type equation \\begin{equation*} -\\Big(a+b\\int_\\Omega|\\nabla u|^2dx\\Big)\\Delta u=f(x,u) \\end{equation*} submitted to Dirichlet boundary conditions. Under a general $4-$superlinear condition on the nonlinearity $f$, we prove the existence of a ground state solution; that is a nontrivial solution which has least energy among the set of nontrivial solutions. In case which $f$ is odd with respect to the second variable, we also obtain the existence of infinitely many solutions. Under our assumptions the Nehari manifold does not need to be of class $\\mathcal{C}^1$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-19T20:52:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35J25"
    ],
    "keywords": [
      "ground state solution",
      "nonlocal boundary-value problem",
      "nontrivial solution",
      "nehari manifold",
      "kirchhoff type equation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.2204B"
    }
  }
}