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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Bourgin-Yang Type Theorem and its application
to $Z_2$-equivariant Hamiltonian systems


Author: Marek Izydorek
Journal: Trans. Amer. Math. Soc. 351 (1999), 2807-2831
MSC (1991): Primary 58E05, 55M20; Secondary 34C25, 34C35
Published electronically: February 24, 1999
MathSciNet review: 1467470
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Abstract | References | Similar Articles | Additional Information

Abstract: We will be concerned with the existence of multiple periodic solutions of asymptotically linear Hamiltonian systems with the presence of $Z_2$-action. To that purpose we prove a new version of the Bourgin-Yang theorem. Using the notion of the crossing number we also introduce a new definition of the Morse index for indefinite functionals.


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Additional Information

Marek Izydorek
Affiliation: Department of Technical Physics and Applied Mathematics, Technical University of Gdańsk, 80-952 Gdańsk, ul. Gabriela Narutowicza 11/12, Poland
Email: izydorek@mifgate.gda.pl

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02144-3
PII: S 0002-9947(99)02144-3
Keywords: Morse index, critical points, periodic solutions, Hamiltonian systems, $Z_2$--genus of space
Received by editor(s): January 9, 1996
Received by editor(s) in revised form: March 7, 1997
Published electronically: February 24, 1999
Article copyright: © Copyright 1999 American Mathematical Society