{
  "id": "1211.2128",
  "version": "v2",
  "published": "2012-11-06T12:41:09.000Z",
  "updated": "2015-01-25T15:18:42.000Z",
  "title": "The splitting lemmas for nonsmooth functionals on Hilbert spaces II. The case at infinity",
  "authors": [
    "Guangcun Lu"
  ],
  "comment": "63 pages. Correcting Section 4 of the published version on [Topological Methods in Nonlinear Analysis, Vol.44, No.2, 2014] because there exist errors in the original one",
  "categories": [
    "math.FA",
    "math.AP",
    "math.GT"
  ],
  "abstract": "We generalize the Bartsch-Li's splitting lemma at infinity for $C^2$-functionals in [2] and some later variants of it to a class of continuously directional differentiable functionals on Hilbert spaces. Different from the previous flow methods our proof is to combine the ideas of the Morse-Palais lemma due to Duc-Hung-Khai [9] with some techniques from [11], [17], [18]. A simple application is also presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-06T12:41:09.000Z",
      "abstract": "We generalize the Bartsch-Li's splitting lemma at infinity for $C^2$-functionals in \\cite{BaLi} and some later variants of it to a class of continuously directional differentiable functionals on Hilbert spaces. Different from the previous flow methods our proof is to combine the ideas of the Morse-Palais lemma due to Duc-Hung-Khai \\cite{DHK} with some techniques from \\cite{JM, Skr, Va1}. A simple application is also presented.",
      "comment": "63 pages. arXiv admin note: original 109 page preprint arXiv:1102.2062 got split into 3 parts-- this is the second one of them which is an improved version of section 4 in 1102.2062 with an application",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-01-25T15:18:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E05",
      "49J52",
      "49J45"
    ],
    "keywords": [
      "hilbert spaces",
      "nonsmooth functionals",
      "continuously directional differentiable functionals",
      "simple application",
      "flow methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 63,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.2128L"
    }
  }
}