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

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

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  • 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.

    Mathematics Subject Classification: 26D10, 34K38.


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