{
  "id": "1808.09148",
  "version": "v1",
  "published": "2018-08-28T07:31:28.000Z",
  "updated": "2018-08-28T07:31:28.000Z",
  "title": "Note on semiclassical states for the Schrödinger equation with nonautonomous nonlinearities",
  "authors": [
    "Bartosz Bieganowski",
    "Jarosław Mederski"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the following Schr\\\"{o}dinger equation $$ - \\hslash ^2 \\Delta u + V(x)u = \\Gamma(x) f(u) \\quad \\mathrm{in} \\ \\mathbb{R}^N, $$ where $u \\in H^1 (\\mathbb{R}^N)$, $u > 0$, $\\hslash > 0$ and $f$ is superlinear and subcritical nonlinear term. We show that if $V$ attains local minimum and $\\Gamma$ attains global maximum at the same point or $V$ attains global minimum and $\\Gamma$ attains local maximum at the same point, then there exists a positive solution for sufficiently small $\\hslash>0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-28T07:31:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35A15",
      "35J20"
    ],
    "keywords": [
      "schrödinger equation",
      "semiclassical states",
      "nonautonomous nonlinearities",
      "attains global maximum",
      "attains local minimum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}