{
  "id": "1112.3159",
  "version": "v1",
  "published": "2011-12-14T10:31:57.000Z",
  "updated": "2011-12-14T10:31:57.000Z",
  "title": "A remark on natural constraints in variational methods and an application to superlinear Schrödinger systems",
  "authors": [
    "Benedetta Noris",
    "Gianmaria Verzini"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "For a regular functional J defined on a Hilbert space X, we consider the set N of points x of X such that the projection of the gradient of J at x onto a closed linear subspace V(x) of X vanishes. We study sufficient conditions for a constrained critical point of J restricted to N to be a free critical point of J, providing a unified approach to different natural constraints known in the literature, such as the Birkhoff-Hestenes natural isoperimetric conditions and the Nehari manifold. As an application, we prove multiplicity of solutions to a class of superlinear Schr\\\"odinger systems on singularly perturbed domains.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-14T10:31:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E05",
      "35A15",
      "35J50"
    ],
    "keywords": [
      "superlinear schrödinger systems",
      "natural constraints",
      "variational methods",
      "application",
      "birkhoff-hestenes natural isoperimetric conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.3159N"
    }
  }
}