Quasiperiodic solutions of semilinear Liénard equations

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 <p align="center"> $ x'' + F_x(x,t)x'+ a^2x + \phi(x) + e(x,t) = 0, $ <p align="left" class="times"> 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.