Quasiperiodic solutions of semilinear Liénard equations

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January 2005, 12(1): 137-160. doi: 10.3934/dcds.2005.12.137

Quasiperiodic solutions of semilinear Liénard equations

1.	LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China

Received June 2003 Revised May 2004 Published December 2004

Abstract
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We deal with the existence of quasi-periodic solutions in classical sense and in the generalized sense, i.e., the existence of invariant tori and Aubry-Mather sets for some semilinear differential equations

$ x'' + F_x(x,t)x'+ a^2x + \phi(x) + e(x,t) = 0, $

where $F$ and $e$ are smooth and $2\pi$-periodic in $t$ and $a>0$ is a constant. As a consequence, we also get the boundedness of all the solutions.

Keywords: quasi-periodic solutions, reversible systems, Aubry-Mather set, Liénard equations., boundedness of solutions.

Mathematics Subject Classification: Primary 34C15, 58F2.

Citation: Bin Liu. Quasiperiodic solutions of semilinear Liénard equations. Discrete & Continuous Dynamical Systems - A, 2005, 12 (1) : 137-160. doi: 10.3934/dcds.2005.12.137

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