Asymptotic Behavior of Solutions of Functional Differential Equations with Finite Delays

AbstractIn this paper we consider a sufficient condition forW(t,x(t)) to approach zero ast→∞, wherex(t) is a solution of a non-autonomous functional differential equation with finite delays andW(t,x) is a so-called Lyapunov function. We shall show that in the applications this provides useful information for asymptotic behavior of the solutionx(t). For example, we generalize examples given by J. R. Haddock and J. Terjéki (J. Differential Equations48, 1983, 95–122) to the case of non-autonomous systems