Sharp estimation for the solutions of delay differential and Halanay type inequalities

István Győri; László Horváth

doi:10.3934/dcds.2017137

Article Contents

2017, Volume 37, Issue 6: 3211-3242. Doi: 10.3934/dcds.2017137

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Sharp estimation for the solutions of delay differential and Halanay type inequalities

István Győri and
László Horváth

Department of Mathematics, University of Pannonia, 8200 Veszprém, Egyetem u. 10., Hungary

Received: September 30, 2016

Revised: December 31, 2016

Published: May 2017

The research of the authors has been supported by Hungarian National Foundations for Scientific Research Grant No. K120186

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Abstract

The present paper develops a framework for a Halanay type nonautonomous delay differential inequality with maxima, and establishes necessary and/or sufficient conditions for the global attractivity of the zero solution. The emphasis is put on the rate of convergence based on the theory of the generalized characteristic equation. The applicability and the sharpness of the results are illustrated by examples. This work aspires to serve as a remarkable step towards a unified theory of the nonautonomous Halanay inequality.

Keywords:

Delay differential inequality,
Halanay inequality,
generalized characteristic equation and inequality.

Mathematics Subject Classification: 26D10, 34K38.

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References

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