ABSTRACT
In classical stability theory of linear ordinary differential equations the research works by Bohl and Perron provide a starting point for the study of the relation ship between stability with respect to permanent perturbances (solvability of the problem on accumulation of perturbations) and asymptotic stability with respect to the initial value. For LFDE with aftereffect this relationship has been treated in a more general way in this chapter. Besides the classical formulation of the problem underwent significant changes. In this chapter, a new specific trend has been proposed in stability theory of FDE with aftereffect, based on the theory of operators in semiordered spaces. Therefore the reader should be aware of some aspects of functional analysis and may omit Chapter 4 at first reading.
