{
  "id": "1308.4320",
  "version": "v2",
  "published": "2013-08-20T14:31:26.000Z",
  "updated": "2014-06-23T10:09:43.000Z",
  "title": "Solutions to a nonlinear Schrödinger equation with periodic potential and zero on the boundary of the spectrum",
  "authors": [
    "Jarosław Mederski"
  ],
  "comment": "To appear in Topol. Methods Nonlinear Anal",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the following nonlinear Schr\\\"odinger equation $$-\\Delta u + V(x) u = g(x,u),$$ where V and g are periodic in x. We assume that 0 is a right boundary point of the essential spectrum of $-\\Delta+V$. The superlinear and subcritical term g satisfies a Nehari type monotonicity condition. We employ a Nehari manifold type technique in a strongly indefitnite setting and obtain the existence of a ground state solution. Moreover we get infinitely many geometrically distinct solutions provided that g is odd.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-23T10:09:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35J10",
      "35J20",
      "58E05"
    ],
    "keywords": [
      "nonlinear schrödinger equation",
      "periodic potential",
      "nehari type monotonicity condition",
      "nehari manifold type technique",
      "right boundary point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.4320M"
    }
  }
}