American Institute of Mathematical Sciences

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

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.

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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