The Conley index in Hilbert spaces and its applications

Volume 134 / 1999

K Gęba, M. Izydorek, A. Pruszko Studia Mathematica 134 (1999), 217-233 DOI: 10.4064/sm-134-3-217-233


We present a generalization of the classical Conley index defined for flows on locally compact spaces to flows on an infinite-dimensional real Hilbert space H generated by vector fields of the form f: H → H, f(x) = Lx + K(x), where L: H → H is a bounded linear operator satisfying some technical assumptions and K is a completely continuous perturbation. Simple examples are presented to show how this new invariant can be applied in searching critical points of strongly indefinite functionals having asymptotically linear gradient.


  • K Gęba
  • M. Izydorek
  • A. Pruszko

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