{
  "id": "1503.07280",
  "version": "v1",
  "published": "2015-03-25T05:08:02.000Z",
  "updated": "2015-03-25T05:08:02.000Z",
  "title": "Schrodinger-Kirchhoff-Poisson type systems",
  "authors": [
    "Cyril J. Batkam",
    "Joao R. Santos Junior"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article we study the existence of solutions to the system \\begin{equation*}\\left\\{ \\begin{array}{ll} -\\left(a+b\\int_{\\Omega}|\\nabla u|^{2}\\right)\\Delta u +\\phi u= f(x, u) &\\text{in }\\Omega \\hbox{} -\\Delta \\phi= u^{2} &\\text{in }\\Omega \\hbox{} u=\\phi=0&\\text{on }\\partial\\Omega, \\hbox{} \\end{array} \\right. \\end{equation*} where $\\Omega$ is a bounded smooth domain of $\\mathbb{R}^N$ ($N=1,2$ or $3$), $a>0$, $b\\geq0$, and $f:\\overline{\\Omega}\\times \\mathbb{R}\\to\\mathbb{R}$ is a continuous function which is $3$-superlinear. By using some variants of the mountain pass theorem established in this paper, we show the existence of three solutions: one positive, one negative, and one which changes its sign. Furthermore, in case $f$ is odd with respect to $u$ we obtain an unbounded sequence of sign-changing solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-25T05:08:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35J47",
      "35B33",
      "35J25",
      "35J50",
      "35J65"
    ],
    "keywords": [
      "schrodinger-kirchhoff-poisson type systems",
      "mountain pass theorem",
      "bounded smooth domain",
      "continuous function",
      "superlinear"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}