Some new results on the stability and boundedness of solutions of certain class of second order vector differential equations

Abstract

In this paper, we provide certain conditions that guarantee the stability of the zero solution when P(t, X, Y) = 0 and boundedness of all solutions when P(t, X, Y) not = 0 of a certain system of second order differential equation using a suitable Lyapunov function. The results in this paper are quite new and complement those in the literature. Examples are given to demonstrate the correctness of the established results.