{
  "id": "1801.01976",
  "version": "v1",
  "published": "2018-01-06T06:43:09.000Z",
  "updated": "2018-01-06T06:43:09.000Z",
  "title": "Standing waves for quasilinear Schröinger equations with indefinite potentials",
  "authors": [
    "Shibo Liu",
    "Jian Zhou"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider quasilinear Schr\\\"{o}dinger equations in $\\mathbb{R}^{N}$ of the form% \\[ -\\Delta u+V(x)u-u\\Delta(u^{2})=g(u)\\text{,}% \\] where $g(u)$ is $4$-superlinear. Unlike all known results in the literature, the Schr\\\"{o}dinger operator $-\\Delta+V$ is allowed to be indefinite, hence the variational functional does not satisfy the mountain pass geometry. By a local linking argument and Morse theory, we obtain a nontrivial solution for the problem. In case that $g$ is odd, we get an unbounded sequence of solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-06T06:43:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "58E05"
    ],
    "keywords": [
      "quasilinear schröinger equations",
      "indefinite potentials",
      "standing waves",
      "mountain pass geometry",
      "variational functional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}