On the Asymptotic Stability of Solutions of Nonlinear Delay Differential Equations

A nonlinear system of delay differential equations (DDEs) is considered. We obtain some new results on the asymptotic stability of a zero solution of the considered system by using well-known inequalities and the Lyapunov–Krasovskii functionals. Two numerical examples illustrate applications of the obtained results. The presented results make contributions to the qualitative theory of DDEs and improve some results known from the modern literature. © 2022, Springer Science+Business Media, LLC, part of Springer Nature.