On nonautonomous functional differential equations

In this paper, we prove a theorem on boundary perturbation of nonautonomous Cauchy problems and then apply this result to show the existence and uniqu eness of classical solutions of the nonautonomous, Banach space valued func tional differential equation {x'(t) = A(t)x(t) + K(t)x(t), 0 less than or equal to t less than or equal to T, {x(tau) = phi(tau - s), s - r less than or equal to tau less than or equal to s. (C) 1999 Academic Press.