Almost periodic and asymptotically almost periodic solutions of Liénard equations

Abstract

The aim of this paper is to study the almost periodic and asymptotically almost periodic solutions on (0, +∞) of the Liénard equationwhere F : T → R (T = R + or R) is an almost periodic or asymptotically almost periodic function and g : (a, b) → R is a strictly decreasing function. We study also this problem for the vectorial Liénard equation.We analyze this problem in the framework of general non-autonomous dynamical systems (cocycles). We apply the general results obtained in our early papers [3,7] to prove the existence of almost periodic (almost automorphic, recurrent, pseudo recurrent) and asymptotically almost periodic (asymptotically almost automorphic, asymptotically recurrent, asymptotically pseudo recurrent) solutions of Liénard equations (both scalar and vectorial).