{
  "id": "math/0402444",
  "version": "v3",
  "published": "2004-02-26T22:41:02.000Z",
  "updated": "2004-04-30T13:56:43.000Z",
  "title": "Sublevel sets and global minima of coercive functionals and local minima of their perturbations",
  "authors": [
    "Biagio Ricceri"
  ],
  "comment": "12 pages",
  "journal": "J. Nonlinear Convex Anal. 5 (2004), no. 2, 157--168",
  "categories": [
    "math.OC"
  ],
  "abstract": "The aim of the present paper is essentially to prove that if $\\Phi$ and $\\Psi$ are two sequentially weakly lower semicontinuous functionals on a reflexive real Banach space and if $\\Psi$ is also continuous and coercive, then then following conclusion holds: if, for some $r > \\inf_X \\Psi$, the weak closure of the set $\\Psi^{-1}(]-\\infty, r[)$ has at least $k$ connected components in the weak topology, then, for each $\\lambda > 0$ small enough, the functional $\\Psi + \\lambda\\Phi$ has at least $k$ local minima lying in $\\Psi^{-1}(]-\\infty, r[)$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-04-30T13:56:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20"
    ],
    "keywords": [
      "local minima",
      "global minima",
      "sublevel sets",
      "coercive functionals",
      "perturbations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2444R"
    }
  }
}