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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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The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems
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by Di Dong and Yiming Long PDF
Trans. Amer. Math. Soc. 349 (1997), 2619-2661 Request permission

Abstract:

In this paper, the iteration formula of the Maslov-type index theory for linear Hamiltonian systems with continuous, periodic, and symmetric coefficients is established. This formula yields a new method to determine the minimality of the period for solutions of nonlinear autonomous Hamiltonian systems via their Maslov-type indices. Applications of this formula give new results on the existence of periodic solutions with prescribed minimal period for such systems, and unify known results under various convexity conditions.
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Additional Information
  • Di Dong
  • Affiliation: Nankai Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
  • Address at time of publication: Department of Mathematics, State University of New York at Stony Brook, Stony Brook, New York 11794-3651
  • Email: ddong@math.sunysb.edu
  • Yiming Long
  • Affiliation: Nankai Institute of Mathematics, Nankai University, Tianjin 300071, People’s Republic of China
  • Email: longym@sun.nankai.edu.cn
  • Received by editor(s): May 3, 1994
  • Additional Notes: The second author was partially supported by YTF of Edu. Comm., NNSF of China, and Qiu Shi Sci. and Tech. Foundations.
  • © Copyright 1997 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 349 (1997), 2619-2661
  • MSC (1991): Primary 58F05, 58E05, 34C25; Secondary 15A18, 15A21
  • DOI: https://doi.org/10.1090/S0002-9947-97-01718-2
  • MathSciNet review: 1373632