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An Optimal Halanay Inequality and Decay Rate of Solutions to Some Classes of Nonlocal Functional Differential Equations

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Abstract

In this work, we prove a nonlocal Halanay inequality with an exact decay rate. This enables us to analyze behavior of solutions to some classes of nonlocal ODEs and PDEs involving unbounded delays. The obtained results extend and improve the previous ones proved for fractional differential equations and other nonlocal subdiffusion equations.

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Acknowledgements

The authors are grateful to the anonymous referee for careful reading the manuscript. The authors would like to thank Hanoi National University of Education for providing a fruitful working environment.

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  1. Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

    Tran Dinh Ke & Nguyen Nhu Thang

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  1. Tran Dinh Ke
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  2. Nguyen Nhu Thang
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Correspondence to Nguyen Nhu Thang.

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Ke, T.D., Thang, N.N. An Optimal Halanay Inequality and Decay Rate of Solutions to Some Classes of Nonlocal Functional Differential Equations. J Dyn Diff Equat (2023). https://doi.org/10.1007/s10884-023-10323-w

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  • DOI: https://doi.org/10.1007/s10884-023-10323-w

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