{
  "id": "1407.6629",
  "version": "v1",
  "published": "2014-07-24T16:05:01.000Z",
  "updated": "2014-07-24T16:05:01.000Z",
  "title": "A multiplicity result for Chern-Simons-Schrödinger equation with a general nonlinearity",
  "authors": [
    "Patricia L. Cunha",
    "Pietro d'Avenia",
    "Alessio Pomponio",
    "Gaetano Siciliano"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we give a multiplicity result for the following Chern-Simons-Schr\\\"odinger equation \\[ -\\Delta u+2q u \\int_{|x|}^{\\infty}\\frac{u^{2}(s)}{s}h_u(s)ds +q u\\frac{h^{2}_u(|x|)}{|x|^{2}} = g(u), \\quad\\hbox{in }\\mathbb{R}^2, \\] where $\\displaystyle h_u(s)=\\int_0^s \\tau u^2(\\tau) \\ d \\tau$, under very general assumptions on the nonlinearity $g$. In particular, for every $n\\in \\mathbb N$, we prove the existence of (at least) $n$ distinct solutions, for every $q\\in (0,q_{n})$, for a suitable $q_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-24T16:05:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35Q55",
      "81T10"
    ],
    "keywords": [
      "multiplicity result",
      "chern-simons-schrödinger equation",
      "general nonlinearity",
      "general assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1307818,
      "adsabs": "2014arXiv1407.6629C"
    }
  }
}