On a development of the comparison principle in the stability theory of motion

Abstract

In this paper, conditions for different types of stability of the zero solution of a nonautonomous nonlinear comparison equation are established, and on this basis the corresponding stability results for the zero solution of the original system of differential equations are obtained. A development of the comparison principle, related to a generalized estimate of the total derivative of a Lyapunov-type auxiliary function with respect to the system under investigation is considered.