Quasiperiodic solutions of semilinear Liénard equations

Bin Liu

doi:10.3934/dcds.2005.12.137

Article Contents

2005, Volume 12, Issue 1: 137-160. Doi: 10.3934/dcds.2005.12.137

This issue Previous Article On the uniqueness of bounded solutions to singular parabolic problems Next Article Two-parameter families of implicit differential equations

Quasiperiodic solutions of semilinear Liénard equations

Bin Liu^1,

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

Received: May 31, 2003

Revised: April 30, 2004

Published: March 2005

Abstract Related Papers Cited by

Abstract

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:

Mathematics Subject Classification: Primary 34C15, 58F27.

Citation:

Article Metrics

HTML views() PDF downloads(92) Cited by(0)

Quasiperiodic solutions of semilinear Liénard equations

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Quasiperiodic solutions of semilinear Liénard equations

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content