The Conley index in Hilbert spaces and its applications
Studia Mathematica, Tome 134 (1999) no. 3, pp. 217-233
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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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author = {K G\k{e}ba and M. Izydorek and A. Pruszko},
title = {The {Conley} index in {Hilbert} spaces and its applications},
journal = {Studia Mathematica},
pages = {217--233},
publisher = {mathdoc},
volume = {134},
number = {3},
year = {1999},
doi = {10.4064/sm-134-3-217-233},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-134-3-217-233/}
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K Gęba; M. Izydorek; A. Pruszko. The Conley index in Hilbert spaces and its applications. Studia Mathematica, Tome 134 (1999) no. 3, pp. 217-233. doi: 10.4064/sm-134-3-217-233
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