Existence of solutions converging to zero for nonlinear delayed differential systems

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 differe...

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Bibliographic Details
Published in:Advances in difference equations 2015-11, Vol.2015 (1), p.1-10, Article 349
Main Authors: Rebenda, Josef, Šmarda, Zdeněk
Format: Article
Language:English
Subjects:
Analysis
Asymptotic properties
Difference and Functional Equations
Difference equations
Differential equations
Functional Analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Ordinary Differential Equations
Partial Differential Equations
Topology
Two dimensional
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Summary: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.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-015-0687-0