A Study of the Asymptotic Behaviour of Solutions of Certain Non-Autonomous Differential Equations of the Fifth Order

Abstract

Sufficient conditions are obtained which ensure that all solutions of the equation x((5)) + f(t, x, <(x)over dot>, <(x)double over dot>, (x) triple over dot, x((4))) + phi(t, <(x)double over dot>, (x) triple over dot) + psi(t, <(x)over dot>, <(x)double over dot>) + g(t, x, <(x)over dot>) + d(t)h(x) = p(t, x, <(x)over dot>, <(x)double over dot>, (x) triple over dot, x((4))) are uniformly bounded and tend to zero as t --> infinity. Our result includes and improves the result obtained in [Appl. Math. Comput. 131 (1) (2002) 1]. (C) 2003 Elsevier Inc. All rights reserved.