{
  "id": "1309.4691",
  "version": "v1",
  "published": "2013-09-18T16:16:23.000Z",
  "updated": "2013-09-18T16:16:23.000Z",
  "title": "Nontrivial solutions for a mixed boundary problem for Schrödinger equations with an external magnetic field",
  "authors": [
    "Claudianor Oliveira Alves",
    "Rodrigo Cohen Mota Nemer",
    "Sérgio Henrique Monari Soares"
  ],
  "comment": "This article is based on the second author's doctoral thesis",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the existence of solutions for a class of nonlinear Schr\\\"odinger equations involving a magnetic field with mixed Dirichlet-Neumann boundary conditions. We use Lyusternik-Shnirelman category and the Morse theory to estimate the number of nontrivial solutions in terms of the topology of the part of the boundary where the Neumann condition is prescribed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-18T16:16:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A15",
      "35H30",
      "35Q55"
    ],
    "keywords": [
      "external magnetic field",
      "mixed boundary problem",
      "nontrivial solutions",
      "schrödinger equations",
      "mixed dirichlet-neumann boundary conditions"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.4691O"
    }
  }
}