{
  "id": "1602.05078",
  "version": "v1",
  "published": "2016-02-16T16:20:17.000Z",
  "updated": "2016-02-16T16:20:17.000Z",
  "title": "Nonlinear Schrödinger equations with sum of periodic and vanishig potentials and sign-changning nonlinearities",
  "authors": [
    "Bartosz Bieganowski",
    "Jarosław Mederski"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We look for ground state solutions to the following nonlinear Schr\\\"odinger equation $$-\\Delta u + V(x)u = f(x,u)-\\Gamma(x)|u|^{q-2}u\\hbox{ on }\\mathbb{R}^N,$$ where $V=V_{per}+V_{loc}\\in L^{\\infty}(\\mathbb{R}^N)$ is the sum of a periodic potential $V_{per}$ and a localized potential $V_{loc}$, $\\Gamma\\in L^{\\infty}(\\mathbb{R}^N)$ is periodic and $\\Gamma(x)\\geq 0$ for a.e. $x\\in\\mathbb{R}^N$ and $2\\leq q<2^*$. We assume that $\\inf\\sigma(-\\Delta+V)>0$, where $\\sigma(-\\Delta+V)$ stands for the spectrum of $-\\Delta +V$ and $f$ has the subcritical growth but higher than $\\Gamma(x)|u|^{q-2}u$, however the nonlinearity $f(x,u)-\\Gamma(x)|u|^{q-2}u$ may change sing. Although a Nehari-type monotonicity condition for the nonlinearity is not satisfied we investigate the existence of ground state solutions being minimizers on the Nehari manifold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-16T16:20:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q60",
      "35J20",
      "35Q55",
      "58E05",
      "35J47"
    ],
    "keywords": [
      "nonlinear schrödinger equations",
      "nonlinearity",
      "vanishig potentials",
      "sign-changning nonlinearities",
      "ground state solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160205078B"
    }
  }
}