On the partial equiasymptotic stability in functional differential equations (Q1604270)

A system of functional-differential equations with delay \(dz/dt=Z(t,z_t)\), where \(Z\) is a 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.