Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Boundedness of solutions for semilinear reversible systems

Author(s): Xiong Li
Journal: Proc. Amer. Math. Soc. 132 (2004), 2057-2066.
MSC (2000): Primary 34C11
Posted: January 20, 2004
MathSciNet review: 2053978
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Abstract | References | Similar articles | Additional information

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

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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