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A Study on Asymptotically Periodic Behavior for Evolution Equations with Delay in Banach Spaces

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Abstract

The goal of this paper is to consider abstract evolution equation with delay in the framework of ordered Banach spaces. Firstly, we investigate the existence of minimal positive S-asymptotically \(\omega \)-periodic mild solution for abstract evolution equation with delay on infinite interval. Secondly, based on monotone iterative technique coupled with fixed point theorem, the existence of minimal positive S-asymptotically \(\omega \)-periodic mild solution is discussed without assuming the existence of upper and lower solutions in the sense of compact and noncompact semigroups. At the end, applications to partial differential equations are given.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No.12061062,11661071). Science Research Project for Colleges and Universities of Gansu Province (No. 2022A-010) Project of NWNU-LKQN2023-02.

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  1. Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Haide Gou & Yongxiang Li

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  1. Haide Gou
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Research supported by NNSF of China (12061062, 11661071), Science Research Project for Colleges and Universities of Gansu Province (No. 2022A-010) and Project of NWNU-LKQN2023-02.

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Gou, H., Li, Y. A Study on Asymptotically Periodic Behavior for Evolution Equations with Delay in Banach Spaces. Qual. Theory Dyn. Syst. 23, 22 (2024). https://doi.org/10.1007/s12346-023-00876-y

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