{
  "id": "0910.5317",
  "version": "v1",
  "published": "2009-10-28T09:38:59.000Z",
  "updated": "2009-10-28T09:38:59.000Z",
  "title": "Convergence of minimax and continuation of critical points for singularly perturbed systems",
  "authors": [
    "Benedetta Noris",
    "Hugo Tavares",
    "Susanna Terracini",
    "Gianmaria Verzini"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a competitive system of two stationary Gross-Pitaevskii equations arising in the theory of Bose-Einstein condensation, and the corresponding scalar equation. We address the question: \"Is it true that every bounded family of solutions of the system converges, as the competition parameter goes to infinity, to a pair which difference solves the scalar equation?\". We discuss this question in the case when the solutions to the system are obtained as minimax critical points via (weak) L^2 Krasnoselskii genus theory. Our results, though still partial, give a strong indication of a positive answer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-28T09:38:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35J50",
      "35Q55"
    ],
    "keywords": [
      "singularly perturbed systems",
      "critical points",
      "convergence",
      "continuation",
      "krasnoselskii genus theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.5317N"
    }
  }
}