## Bourgin-Yang type theorem and its application to $Z_2$-equivariant Hamiltonian systems

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- by Marek Izydorek
- Trans. Amer. Math. Soc.
**351**(1999), 2807-2831 - DOI: https://doi.org/10.1090/S0002-9947-99-02144-3
- Published electronically: February 24, 1999
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## 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.## References

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## Bibliographic 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
- Received by editor(s): January 9, 1996
- Received by editor(s) in revised form: March 7, 1997
- Published electronically: February 24, 1999
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1467470