On the Sharpness of a Theorem by Cooke and Verduyn Lunel

The sharpness of a theorem of K. Cooke and S. M. Verduyn Lunel Differential Integral Equations 6 1993. 1101]1117. about small solutions of linear timedependent delay equations is proved. A wide class of nonautonomous functionaldifferential equations possessing small solutions is constructed. The construction is based on the existence of quickly decreasing solutions of functional-differential equations with linearly expanded arguments. Q 1996 Academic Press, Inc.