Stability of abstract nonlinear nonautonomous differential–delay equations with unbounded history-responsive operators

We consider a class of nonautonomous functional–differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input–output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.  2004 Elsevier Inc. All rights reserved