On the Partial Equiasymptotic Stability in Functional Differential Equations

A system of functional differential equations with delay dz/dt = Z t zt , 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.