Abstract
In this paper, a class of nonlinear and nonautonomous neutral functional differential equations is considered. By developing a new integral inequality, we obtain sufficient conditions for the existence of a global attracting set of neutral functional differential equations with time-varying delays. The results have extended and improved the related reports in the literature.
Highlights
The asymptotic properties of neutral functional differential equations have attracted considerable attention in the past few decades, and many significant results have been obtained [ – ]
One of the most popular ways to analyze the stability property and asymptotic behavior is the method of Lyapunov functionals [ – ]
Motivated by the above discussions, in this paper, we will improve the inequality established in [ ] so that it is effective for neutral functional differential equations
Summary
1 Introduction The asymptotic properties of neutral functional differential equations have attracted considerable attention in the past few decades, and many significant results have been obtained [ – ]. It seems to work well for constant delays in neutral equations [ , ]. The known approach to the study of differential inequalities for nonautonomous neutral functional differential equations was presented in Azbelev’s book [ ].
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