SOME RESULTS ON STABILITY OF RETARDED FUNCTIONAL-DIFFERENTIAL EQUATIONS USING DICHOTOMIC MAP TECHNIQUES

This paper deals with the study of the stability of nonautonomous reta rded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and as ymptotic stability. Some examples are given to illustrate the applicat ion of the method. Main results about asymptotic stability of the equa tion x'(t) = -b(t)x(t - r) and of its nonlinear generalization x'(t) = b(t)f(x(t - r)) are established.