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

Quasiperiodic solutions of semilinear Liénard equations

Bin Liu 1,

1. 

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

Received  June 2003 Revised  May 2004 Published  December 2004

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