Stability and Ultimate Boundedness for Non-Autonomous System With Variable Delay

Abstract

In this paper, we investigate proper sufficient conditions for the uniform stability (US) of the zero solution, and for the uniform boundedness (UB) as well as uniform ultimate boundedness (UUB) of all solutions of a certain system of nonlinear nonautonomous third-order differential equation (DE) with variable delay. In the proofs, the method of Lyapunov functional (LF) approach is employed as a main tool and two examples are presented in the last section to show feasibility of the established results which improve the results of the previous pieces of literature. © 2020 NSP Natural Sciences Publishing Cor.