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

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 with 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/instability conditions depend closely on the parametrization of the original differential equation.