Boundedness of solutions for semilinear reversible systems

Author:
Xiong Li

Translated by:

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2057-2066

MSC (2000):
Primary 34C11

DOI:
https://doi.org/10.1090/S0002-9939-04-07284-3

Published electronically:
January 20, 2004

MathSciNet review:
2053978

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Abstract: In this paper we will study the boundedness of all solutions for second-order differential equations

where and satisfies the sublinear growth condition. Since the system in general is non-Hamiltonian, we have to introduce reversibility assumptions to apply the twist theorem for reversible mappings. Under some suitable conditions we then obtain the existence of invariant tori and thus the boundedness of all solutions.

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Additional Information

**Xiong Li**

Affiliation:
Department of Mathematics, Beijing Normal University, Beijing 100875, People’s Republic of China

Email:
xli@bnu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-04-07284-3

Keywords:
Boundedness of solutions,
KAM theory,
reversible systems

Received by editor(s):
November 5, 2002

Received by editor(s) in revised form:
March 2, 2003, and March 21, 2003

Published electronically:
January 20, 2004

Additional Notes:
This project (10301006) was supported by the NSFC

Communicated by:
Carmen C. Chicone

Article copyright:
© Copyright 2004
American Mathematical Society