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Paper   IPM / M / 446
School of Mathematics
  Title:   Ljusternik-Schnirelmann theory and Conley index, a noncompact version
  Author(s):  M. R. Razvan
  Status:   Published
  Journal: Asian J. Math.
  No.:  2
  Vol.:  4
  Year:  2000
  Pages:   383-390
  Supported by:  IPM
In this paper we use a noncompact version of Conley index theory to obtain a Ljusternik-Schnirelmann type result in critical point theory: Let X be a complete Finsler manifold, fC1(X,\BbbR) which satisfies Palais-Smale condition and φt be the flow relative to a pseudo-gradient vector field for f. If IX is a (c)-invariant set with f(I) bounded, then f has at least νH(h(I))−1 critical points in I where νH is the (homotopy) Ljusternik-Schnirelmann category and h(I) is the Conley index of I.

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