Existence of solutions converging to zero for nonlinear delayed differential systems

Abstract

We present a result about an interesting asymptotic property of real two-dimensional delayed differential systems satisfying certain sufficient conditions. We employ two previous results, which were obtained using a Razumikhin-type modification of the Ważewski topological method for retarded differential equations and the method of a Lyapunov-Krasovskii functional. The result is illustrated by a nontrivial explanatory example.