Asymptotic Behavior of Solutions of Functional Differential Equations with Finite Delays

In this paper we consider a sufficient condition for W t, x t..to approach zero as tª`, where x t. is a solution of a non-autonomous functional differential equation with finite delays and W t, x.is a so-called Lyapunov function. We shall show that in the applications this provides useful information for asymptotic behavior of the solution x t.. For example, we generalize examples given by J. R. Haddock and J. Terj´eki J. Differential Equations 48, 1983, 95]122.to the case of non-autonomous systems.