On the stability and vibrational stabilization of a class of nonlinear systems

A certain class of nonlinear oscillatory systems is investigated. The method of construction of Lyapunov's functions is suggested to obtain sufficient conditions of asymptotic stability and instability of the equilibrium position for systems considered. The influence of the nonautonomous perturbations on the asymptotic behavior of solutions is studied. The conditions under which the equilibrium position may be stabilized by means of the periodic variations of system parameters are investigated.