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Stability for Nonautonomous Linear Differential Systems with Infinite Delay

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Abstract

We study the stability of general n-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first situation, the effect of the delays is dominated by non-delayed diagonal negative feedback terms, and sufficient conditions for both the asymptotic and the exponential asymptotic stability of the system are given. In the second case, the stability depends on the size of some bounded diagonal delays and coefficients, although terms with unbounded delay may co-exist. Our results encompass DDEs with discrete and distributed delays, and enhance some recent achievements in the literature.

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Acknowledgements

This work was supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia (Portugal) under project UIDB/04561/2020.

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  1. Departamento de Matemática and CMAF-CIO, Faculdade de Ciências, Universidade de Lisboa, 1749-016, Campo Grande, Lisbon, Portugal

    Teresa Faria

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  1. Teresa Faria
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Correspondence to Teresa Faria.

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To the memory of Professor Russell A. Johnson.

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Faria, T. Stability for Nonautonomous Linear Differential Systems with Infinite Delay. J Dyn Diff Equat 34, 747–773 (2022). https://doi.org/10.1007/s10884-020-09873-0

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  • DOI: https://doi.org/10.1007/s10884-020-09873-0

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