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The Conley index in Hilbert spaces and its applications

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Gęba K., Izydorek M., Pruszko A.

Studia Mathematica

1999

tom 134

nr 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.

Ograniczanie wyników

1 Studia Mathematica

1 Gęba K.

1 Izydorek M.

1 Pruszko A.

1 1999

Wyniki wyszukiwania

The Conley index in Hilbert spaces and its applications