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June  2021, 26(6): 2921-2939. doi: 10.3934/dcdsb.2020211

## Periodic solutions to non-autonomous evolution equations with multi-delays

 Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received  March 2020 Revised  April 2020 Published  July 2020

Fund Project: Research supported by National Natural Science Foundations of China (No. 11501455, No. 11661071), Project of NWNU-LKQN2019-3 and China Scholarship Council (No. 201908625016)

In this paper, we provide some sufficient conditions for the existence, uniqueness and asymptotic stability of time $\omega$-periodic mild solutions for a class of non-autonomous evolution equation with multi-delays. This work not only extend the autonomous evolution equation with multi-delays studied in [37] to non-autonomous cases, but also greatly weaken the condition presented in [37] even for the case $a(t)\equiv a$ by establishing a general abstract framework to find time $\omega$-periodic mild solutions for non-autonomous evolution equation with multi-delays. Finally, one illustrating example is supplied.

Citation: Pengyu Chen. Periodic solutions to non-autonomous evolution equations with multi-delays. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2921-2939. doi: 10.3934/dcdsb.2020211
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