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Periodicity of Solutions for Non-Autonomous Neutral Functional Differential Equations with State-Dependent Delay

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Abstract

This paper is concerned with the existence of solutions and periodic solutions for a class of semilinear neutral functional differential equations with state-dependent delay, in which the linear part is non-autonomous and generates a linear evolution operator. We first establish the existence and regularity of bounded solutions for the considered equation, and then we show by using Banach fixed point theorem that these solutions have periodicity property or asymptotic periodicity property respectively under some conditions . Finally, an example to illustrate the obtained results is given.

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Acknowledgements

We would like to thank the referees greatly for the careful review and the important suggestions to this paper.

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Authors and Affiliations

  1. College of Mathematics Science, Inner Mongolia Normal University, Hohhot, 010022, People’s Republic of China

    Jianbo Zhu

  2. School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, People’s Republic of China

    Xianlong Fu

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  1. Jianbo Zhu
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  2. Xianlong Fu
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Correspondence to Xianlong Fu.

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This work is supported by NSF of China (Nos. 11671142 and 11771075), Science and Technology Commission of Shanghai Municipality (STCSM) (Grant No. 18dz2271000)

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Zhu, J., Fu, X. Periodicity of Solutions for Non-Autonomous Neutral Functional Differential Equations with State-Dependent Delay. J Dyn Diff Equat 35, 1389–1408 (2023). https://doi.org/10.1007/s10884-021-10098-y

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  • DOI: https://doi.org/10.1007/s10884-021-10098-y

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