Convergence in asymptotically autonomous functional differential equations

In this paper, we consider linear and nonlinear perturbations of a linear a utonomous functional differential equation which has infinitely many equili bria. We give sufficient conditions under which the solutions of the pertur bed equation tend to the equilibria of the unperturbed equation at infinity . As a consequence, we obtain sufficient conditions for systems of delay di fferential equations to have asymptotic equilibrium. (C) 1999 Academic Pres s.