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 = H(Y), ?Y = -F(X, Y)Y - G(X) + P(t,X, Y), where t 2 R+, X = X(t), Y = Y (t) 2 Rn, F: Rn × Rn ! Rn×n, G,H: Rn ! Rn and P: R+×Rn×Rn ! Rn. 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. [ABSTRACT FROM AUTHOR]