On the Partial Equiasymptotic Stability in Functional Differential Equations

Abstract

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.  2002 Elsevier Science (USA)

On stability in terms of two measures for impulsive systems of functional differential equations

“…, y(t)) T , then (4.1) is (h 0 , h)-equi-AS reduces to the trivial solution of (4.1) is equiasymptotically x-stable (see [5,8]). …”

Asymptotic stability and instability with respect to part of variables for solutions to impulsive systems

“…The basics of the theory of stability with respect to part of variables for the models described by ordinary differential equations can be found in [1][2][3][4]. A series of later articles was devoted to stability of the motions with respect to part of variables which were described by delay functional differential equations (for example, see [5][6][7][8]). In the mathematical description of evolution of the actual processes with perturbations of short duration it is convenient in many cases to neglect the duration of perturbations and assume that these perturbations are of an "instantaneous" character.…”

Partially equi-integral ϕ0-stability of nonlinear differential systems

“…El-Sheikh et al [2] justified the partial stability of nonlinear differential systems. Ignatyev [6] studied the partial equi-asymptotical stability of functional differential equations.…”