Abstract. In this paper, sufficient criteria for the existence of solutions to uniform asymptotic stability and boundedness problems associated with certain second order nonlinear non autonomous ordinary differential equation are established with the aid of Lyapunov's direct method. Furthermore, the appropriate complete Lyapunov function is given explicitly. Our results complement some well known results on the second order differential equations in the literature.

In this study, we established sufficient criteria for uniform asymptotic stability and boundedness of solutions of certain class of second order nonlinear non autonomous ordinary differential equations using a complete Lyapunov function. Our results extend some existing one in the literature.

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