{
  "id": "1901.03187",
  "version": "v1",
  "published": "2019-01-09T01:05:58.000Z",
  "updated": "2019-01-09T01:05:58.000Z",
  "title": "Berestycki-Lions conditions on ground state solutions for Kirchhoff-type problems with variable potentials",
  "authors": [
    "Sitong Chen",
    "Xianhua Tang"
  ],
  "comment": "This paper was submitted to Journal on April 18, 2018. arXiv admin note: substantial text overlap with arXiv:1803.01130",
  "categories": [
    "math.AP"
  ],
  "abstract": "By introducing some new tricks, we prove that the nonlinear problem of Kirchhoff-type \\begin{equation*} \\left\\{ \\begin{array}{ll} -\\left(a+b\\int_{\\R^3}|\\nabla u|^2\\mathrm{d}x\\right)\\triangle u+V(x)u=f(u), & x\\in \\R^3; u\\in H^1(\\R^3), \\end{array} \\right. \\end{equation*} admits two class of ground state solutions under the general \"Berestycki-Lions assumptions\" on the nonlinearity $f$ which are almost necessary conditions, as well as some weak assumptions on the potential $V$. Moreover, we also give a simple minimax characterization of the ground state energy. Our results improve and complement previous ones in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-09T01:05:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35Q55"
    ],
    "keywords": [
      "ground state solutions",
      "kirchhoff-type problems",
      "berestycki-lions conditions",
      "variable potentials",
      "simple minimax characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}