## 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.## References

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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