# The Conley index in Hilbert spaces and its applications

K. Gęba; M. Izydorek; A. Pruszko

Studia Mathematica (1999)

- Volume: 134, Issue: 3, page 217-233
- ISSN: 0039-3223

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topGęba, K., Izydorek, M., and Pruszko, A.. "The Conley index in Hilbert spaces and its applications." Studia Mathematica 134.3 (1999): 217-233. <http://eudml.org/doc/216635>.

@article{Gęba1999,

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.},

author = {Gęba, K., Izydorek, M., Pruszko, A.},

journal = {Studia Mathematica},

keywords = {Conley index; asymptotically linear Hamiltonian systems; periodic solutions},

language = {eng},

number = {3},

pages = {217-233},

title = {The Conley index in Hilbert spaces and its applications},

url = {http://eudml.org/doc/216635},

volume = {134},

year = {1999},

}

TY - JOUR

AU - Gęba, K.

AU - Izydorek, M.

AU - Pruszko, A.

TI - The Conley index in Hilbert spaces and its applications

JO - Studia Mathematica

PY - 1999

VL - 134

IS - 3

SP - 217

EP - 233

AB - 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.

LA - eng

KW - Conley index; asymptotically linear Hamiltonian systems; periodic solutions

UR - http://eudml.org/doc/216635

ER -

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