NEW RESULT ON THE ULTIMATE BOUNDEDNESS OF SOLUTIONS FOR CERTAIN FIFTH-ORDER NON-AUTONOMOUS DELAY DIFFERENTIAL EQUATION

This paper studies the boundedness of solution x(t) of the fifth-order nonlinear delay differential equation x((5))(t) + psi(t, x(t - r), <(x)single over dot>(t - r), <(x)double over dot>(t - r), (x) triple over dot (t - r), x((4))(t - r))x((4))(t) + f((x) triple over dot (t - r)) + alpha(3)<(x)double over dot>(t) + alpha(4)<(x)single over dot>(t) + alpha(5)x(t) = p(t, x(t - r), <(x)single over dot>(t - r), <($)double over dot>(t - r), (x) triple over dot (t - r), x((4))(t - r)). Sufficient conditions for the boundedness of solutions are obtained by constructing a Lyapunov functional.