{
  "id": "1806.08510",
  "version": "v1",
  "published": "2018-06-22T06:30:30.000Z",
  "updated": "2018-06-22T06:30:30.000Z",
  "title": "Nondegeneracy of positive solutions to a Kirchhoff problem with critical Sobolev growth",
  "authors": [
    "Gongbao Li",
    "Chang-Lin Xiang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we prove uniqueness and nondegeneracy of positive solutions to the following Kirchhoff equations with critical growth \\begin{eqnarray*} -\\left(a+b\\int_{\\mathbb{R}^{3}}|\\nabla u|^{2}\\right)\\Delta u=u^{5}, & u>0 & \\text{in }\\mathbb{R}^{3},\\end{eqnarray*} where $a,b>0$ are positive constants. This result has potential applications in singular perturbation problems concerning Kirchhoff equaitons.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-22T06:30:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical sobolev growth",
      "positive solutions",
      "kirchhoff problem",
      "nondegeneracy",
      "singular perturbation problems concerning kirchhoff"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}