Existence and asymptotic behavior of square-mean $ S $-asymptotically periodic solutions of fractional stochastic evolution equations

Qiang Li; Lishan Liu

doi:10.3934/dcdss.2023067

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2024, Volume 17, Issue 2: 664-689. Doi: 10.3934/dcdss.2023067

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Existence and asymptotic behavior of square-mean $ S $-asymptotically periodic solutions of fractional stochastic evolution equations

Qiang Li^1, and
Lishan Liu^2, ,

1.
College of Mathematics and Statistics, Qinghai Normal University, Xining 810000, China
2.
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

^*Corresponding author: Lishan Liu
^*Corresponding author: Lishan Liu

Dedicated to Professor Yihong Du on the Occasion of His 60th Birthday.

Received: December 2022

Revised: March 2023

Early access: March 30, 2023

Published online: March 30, 2023

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Abstract

This paper investigates the abstract fractional stochastic evolution equations. A new existence result of the square-mean $ S $-asymptotically periodic mild solutions are obtained under the assumption that the nonlinear terms only satisfy some growth conditions. Moreover, the uniqueness and asymptotic stability results of the square-mean $ S $-asymptotically periodic solution are presented when the nonlinear functions satisfy the general Lipschitz condition. Finally, two examples are given to illustrate our main results.

Keywords:

Fractional stochastic evolution equation,
square-mean S-asymptotically periodic solutions,
existence,
asymptotic behavior,
semigroup.

Mathematics Subject Classification: 60H15, 47D06, 34G20, 46T20.

Citation:

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