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

Pengyu Chen

doi:10.3934/dcdsb.2020211

Article Contents

2021, Volume 26, Issue 6: 2921-2939. Doi: 10.3934/dcdsb.2020211

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

Pengyu Chen

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

Received: February 29, 2020

Revised: March 31, 2020

Early access: July 2020

Published: June 2021

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

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Abstract

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.

Keywords:

Non-autonomous evolution equation with multi-delays,
Periodic solution,
Existence and uniqueness,
Asymptotic stability,
Evolution family.

Mathematics Subject Classification: Primary 34K13; Secondary 35K57, 47J35.

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