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

Abstract

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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.

How to cite

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Gęba, 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 -

References

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