Bourgin-Yang Type Theorem and its application

to -equivariant Hamiltonian systems

Author:
Marek Izydorek

Journal:
Trans. Amer. Math. Soc. **351** (1999), 2807-2831

MSC (1991):
Primary 58E05, 55M20; Secondary 34C25, 34C35

DOI:
https://doi.org/10.1090/S0002-9947-99-02144-3

Published electronically:
February 24, 1999

MathSciNet review:
1467470

Full-text PDF

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 -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:
https://doi.org/10.1090/S0002-9947-99-02144-3

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