{
  "id": "1404.0771",
  "version": "v1",
  "published": "2014-04-03T06:23:04.000Z",
  "updated": "2014-04-03T06:23:04.000Z",
  "title": "Existence of nontrivial solutions for periodic Schrodinger equations with new nonlinearities",
  "authors": [
    "Shaowei Chen",
    "Dawei Zhang"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1310.2399",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the Schr\\\"{o}dinger equation: \\begin{eqnarray} - \\Delta u+V(x)u+f(x,u)=0,\\qquad u\\in H^{1}(\\mathbb{R}^{N}),\\nonumber \\end{eqnarray} where $V$ is periodic and $f$ is periodic in the $x$-variables, $0$ is in a gap of the spectrum of the operator $-\\Delta+V$. We prove that under some new assumptions for $f$, this equation has a nontrivial solution. Our assumptions for the nonlinearity $f$ are very weak and greatly different from the known assumptions in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-03T06:23:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic schrodinger equations",
      "nontrivial solution",
      "nonlinearity",
      "assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.0771C"
    }
  }
}