STABILITY OF PERIODIC SOLUTIONS IN
LIPSCHITZ SYSTEMS WITH A SMALL PARAMETER
In this paper we study the existence, uniqueness and asymptotic stability of the periodic solutions for Lipschitz systems written in the standard form for averaging. Classical hypotheses in the periodic case of second Bogolyubov's theorem imply our ones. By means of the results established we construct the curves of dependence of the amplitude of asymptotically stable periodic solutions on parameters of a forced asymmetric oscillator.