Existence of bounded solutions for inhomogeneous linear delay equations

Abstract

In this paper, we consider a non-autonomous inhomogeneous linear retarded functional differential equations where the forcing term is a bounded continuous function. We show that a sufficient condition which ensure the existence of bounded solutions of the delay system is the property of exponential dichotomy of the solution operator of the homogeneous system associated. We use the sun-star framework and the perturbation theory for dual semigroups.