On the partial equiasymptotic stability in functional differential equations

A system of functional differential equations with delay dz/dt = Z(t, z(t)), where Z is the vector-valued functional is considered. It is supposed that this system has a zero solution z = 0. Definitions of its partial stability, partial asymptotical stability, and partial equiasymptotical stability are given. Theorems on the partial equiasymptotical stability are formulated and proved. (C) 2002 Elsevier Science (USA).