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 time-dependent delay equations is proved. A wide class of nonautonomous functional-differential 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.
ASJC Scopus subject areas
- Applied Mathematics