{
  "id": "1107.5652",
  "version": "v2",
  "published": "2011-07-28T09:03:34.000Z",
  "updated": "2012-03-09T16:57:56.000Z",
  "title": "Semi-classical states for the Nonlinear Schrödinger Equation on saddle points of the potential via variational methods",
  "authors": [
    "Pietro d'Avenia",
    "Alessio Pomponio",
    "David Ruiz"
  ],
  "comment": "pre-peer version, to appear in J. Funct. Anal",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study semiclassical states for the problem $$ -\\eps^2 \\Delta u + V(x) u = f(u) \\qquad \\hbox{in} \\RN,$$ where $f(u)$ is a superlinear nonlinear term. Under our hypotheses on $f$ a Lyapunov-Schmidt reduction is not possible. We use variational methods to prove the existence of spikes around saddle points of the potential $V(x)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-03-09T16:57:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35B40"
    ],
    "keywords": [
      "nonlinear schrödinger equation",
      "saddle points",
      "variational methods",
      "semi-classical states",
      "superlinear nonlinear term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.5652D"
    }
  }
}