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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
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

\begin{displaymath}\ddot{x} + f(x)\dot{x} +\lambda^2 x+ g(x)=p(t),\end{displaymath}

where $\lambda\in R$ and $g(x)$ 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

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

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