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Title

The Conley index in Hilbert spaces and its applications

Authors 1, 1, 1

Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, 18 Abrahama St., 81-825 Sopot, Poland.

Abstract

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.

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Studia Mathematica
1999/134/3
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Pages:
217-233
Main language of publication
English
Received
1997-11-17
Accepted
1998-10-02
Published
1999
Exact and natural sciences