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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Bourgin-Yang type theorem and its application to $Z_2$-equivariant Hamiltonian systems
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by Marek Izydorek PDF
Trans. Amer. Math. Soc. 351 (1999), 2807-2831 Request permission

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
  • 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