{
  "id": "1606.08471",
  "version": "v1",
  "published": "2016-06-27T20:16:07.000Z",
  "updated": "2016-06-27T20:16:07.000Z",
  "title": "Fractional NLS equations with magnetic field, critical frequency and critical growth",
  "authors": [
    "Zhang Binlin",
    "Marco Squassina",
    "Zhang Xia"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The paper is devoted to the study of a singularly perturbed fractional Schr\\\"{o}dinger equations involving critical frequency and critical growth in the presence of a magnetic field. By using variational methods, we obtain the existence of mountain pass solutions $u_{\\varepsilon}$ which tend to the trivial solution as $\\varepsilon\\rightarrow0$. Moreover, we get infinitely many solutions and sign-changing solutions for the problem in absence of magnetic effects under some extra assumptions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-27T20:16:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R11",
      "35J62",
      "35B33",
      "35A15"
    ],
    "keywords": [
      "fractional nls equations",
      "magnetic field",
      "critical growth",
      "critical frequency",
      "mountain pass solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}