{
  "id": "1908.08369",
  "version": "v1",
  "published": "2019-08-22T13:38:45.000Z",
  "updated": "2019-08-22T13:38:45.000Z",
  "title": "Existence and multiplicity results for a new $p(x)$-Kirchhoff problem",
  "authors": [
    "M. K. Hamdani",
    "A. Harrabi",
    "F. Mtiri",
    "D. D. Repovš"
  ],
  "journal": "Nonlinear Anal. 190 (2020), art. 111598, 15 pp",
  "doi": "10.1016/j.na.2019.111598",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the existence and multiplicity results for the following nonlocal $p(x)$-Kirchhoff problem: \\begin{equation} \\label{10} \\begin{cases} -\\left(a-b\\int_\\Omega\\frac{1}{p(x)}| \\nabla u| ^{p(x)}dx\\right)div(|\\nabla u| ^{p(x)-2}\\nabla u)=\\lambda |u| ^{p(x)-2}u+g(x,u) \\mbox{ in } \\Omega, \\\\ u=0,\\mbox{ on } \\partial\\Omega, \\end{cases} \\end{equation} where $a\\geq b > 0$ are constants, $\\Omega\\subset \\mathbb{R}^N$ is a bounded smooth domain, $p\\in C(\\overline{\\Omega})$ with $N>p(x)>1$, $\\lambda$ is a real parameter and $g$ is a continuous function. The analysis developed in this paper proposes an approach based on the idea of considering a new nonlocal term which presents interesting difficulties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-22T13:38:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35J55",
      "35J65"
    ],
    "keywords": [
      "kirchhoff problem",
      "multiplicity results",
      "bounded smooth domain",
      "nonlocal term",
      "real parameter"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}