{
  "id": "1905.04542",
  "version": "v1",
  "published": "2019-05-11T15:36:22.000Z",
  "updated": "2019-05-11T15:36:22.000Z",
  "title": "Bound states for the Schrödinger equation with mixed-type nonlinearites",
  "authors": [
    "Bartosz Bieganowski",
    "Jarosław Mederski"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the existence results for the Schr\\\"odinger equation of the form $$ -\\Delta u + V(x) u = g(x,u), \\quad x \\in \\mathbb{R}^N, $$ where $g$ is superlinear and subcritical in some periodic set $K$ and linear in $\\mathbb{R}^N \\setminus K$ for sufficiently large $|u|$. The periodic potential $V$ is such that $0$ lies in a spectral gap of $-\\Delta+V$. We find a solution with the energy bounded by a certain min-max level, and infinitely many geometrically distinct solutions provided that $g$ is odd in $u$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-11T15:36:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35Q60",
      "35A15",
      "35J20",
      "58E05"
    ],
    "keywords": [
      "schrödinger equation",
      "mixed-type nonlinearites",
      "bound states",
      "periodic set",
      "existence results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}