{
  "id": "1907.01888",
  "version": "v1",
  "published": "2019-07-03T12:34:24.000Z",
  "updated": "2019-07-03T12:34:24.000Z",
  "title": "Infinitely many sign-changing solutions for Kirchhoff type problems in $\\mathbb{R}^3$",
  "authors": [
    "Jijiang Sun",
    "Lin Li",
    "Matija Cencelj",
    "Boštjan Gabrovšek"
  ],
  "journal": "Nonlinear Analysis, vol. 186, 2019, pages 33-54",
  "doi": "10.1016/j.na.2018.10.007",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the following nonlinear Kirchhoff type problem: \\[ \\left\\{\\begin{array}{lcl}-\\left(a+b\\displaystyle\\int_{\\mathbb{R}^3}|\\nabla u|^2\\right)\\Delta u+V(x)u=f(u), & \\textrm{in}\\,\\,\\mathbb{R}^3,\\\\ u\\in H^1(\\mathbb{R}^3), \\end{array}\\right. \\] where $a,b>0$ are constants, the nonlinearity $f$ is superlinear at infinity with subcritical growth and $V$ is continuous and coercive. For the case when $f$ is odd in $u$ we obtain infinitely many sign-changing solutions for the above problem by using a combination of invariant sets method and the Ljusternik-Schnirelman type minimax method. To the best of our knowledge, there are only few existence results for this problem. It is worth mentioning that the nonlinear term may not be 4-superlinear at infinity, in particular, it includes the power-type nonlinearity $|u|^{p-2}u$ with $p\\in(2,4]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-03T12:34:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sign-changing solutions",
      "nonlinear kirchhoff type problem",
      "ljusternik-schnirelman type minimax method",
      "invariant sets method",
      "nonlinear term"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}