Boundedness Of Certain System Of Second Order Differential Equations

This work is concerned with the ultimate boundedness of solutions of the system of vector differential equations(X)over dot = H(Y), (Y)over dot = -F(X, Y)Y - G(X) + P(t, X, Y),where t is an element of R+, X = X(t), Y = Y(t) is an element of R-n, F : R-n x R-n -> R-nxn, G, H : R-n -> R-n and P : R+ x R-n x R-n -> R-n. By using a Lyapunov function as a basic technique, we prove that the solutions of the system of equations are ultimately bounded. In addition, result obtained includes and improves some related results in literature.