On the stability and instability of a class of nonlinear nonautonomous ordinary differential equations

摘要

This paper presents sufficient conditions for Lyapunov' s stability and instability of a class of nonlinear nonautonomous second-order ordinary differential equations. Such a class includes as particular cases a remarkably large number of differential equations wit specific physical applications. Two successive nonlinear transformations are applied to the original differential equation in order to convert it into a more convenient form for stability analysis purposes. The obtained stability I instability conditions depend closely on the parametrization of the original differential equation.