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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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##### References:
 [1] Mahesh G. Nerurkar. Spectral and stability questions concerning evolution of non-autonomous linear systems. Conference Publications, 2001, 2001 (Special) : 270-275. doi: 10.3934/proc.2001.2001.270 [2] K. Ravikumar, Manil T. Mohan, A. Anguraj. Approximate controllability of a non-autonomous evolution equation in Banach spaces. Numerical Algebra, Control & Optimization, 2021, 11 (3) : 461-485. doi: 10.3934/naco.2020038 [3] Qiang Li, Mei Wei. Existence and asymptotic stability of periodic solutions for neutral evolution equations with delay. Evolution Equations & Control Theory, 2020, 9 (3) : 753-772. doi: 10.3934/eect.2020032 [4] Tomás Caraballo, P.E. Kloeden. Non-autonomous attractors for integro-differential evolution equations. Discrete & Continuous Dynamical Systems - S, 2009, 2 (1) : 17-36. doi: 10.3934/dcdss.2009.2.17 [5] Pengyu Chen, Xuping Zhang. Approximate controllability of nonlocal problem for non-autonomous stochastic evolution equations. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020076 [6] Peter E. Kloeden, Jacson Simsen. Pullback attractors for non-autonomous evolution equations with spatially variable exponents. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2543-2557. doi: 10.3934/cpaa.2014.13.2543 [7] Pengyu Chen. Non-autonomous stochastic evolution equations with nonlinear noise and nonlocal conditions governed by noncompact evolution families. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2725-3737. doi: 10.3934/dcds.2020383 [8] Pengyu Chen, Yongxiang Li, Xuping Zhang. Cauchy problem for stochastic non-autonomous evolution equations governed by noncompact evolution families. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1531-1547. doi: 10.3934/dcdsb.2020171 [9] Saulo R.M. Barros, Antônio L. Pereira, Cláudio Possani, Adilson Simonis. Spatially periodic equilibria for a non local evolution equation. Discrete & Continuous Dynamical Systems, 2003, 9 (4) : 937-948. doi: 10.3934/dcds.2003.9.937 [10] Abdelaziz Rhandi, Roland Schnaubelt. Asymptotic behaviour of a non-autonomous population equation with diffusion in $L^1$. Discrete & Continuous Dynamical Systems, 1999, 5 (3) : 663-683. doi: 10.3934/dcds.1999.5.663 [11] Hongmei Cheng, Rong Yuan. Existence and asymptotic stability of traveling fronts for nonlocal monostable evolution equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 3007-3022. doi: 10.3934/dcdsb.2017160 [12] Xianlong Fu. Approximate controllability of semilinear non-autonomous evolution systems with state-dependent delay. Evolution Equations & Control Theory, 2017, 6 (4) : 517-534. doi: 10.3934/eect.2017026 [13] Pengyu Chen, Xuping Zhang. Non-autonomous stochastic evolution equations of parabolic type with nonlocal initial conditions. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020308 [14] Tôn Việt Tạ. Non-autonomous stochastic evolution equations in Banach spaces of martingale type 2: Strict solutions and maximal regularity. Discrete & Continuous Dynamical Systems, 2017, 37 (8) : 4507-4542. doi: 10.3934/dcds.2017193 [15] Mustapha Mokhtar-Kharroubi. On permanent regimes for non-autonomous linear evolution equations in Banach spaces with applications to transport theory. Kinetic & Related Models, 2010, 3 (3) : 473-499. doi: 10.3934/krm.2010.3.473 [16] Aníbal Rodríguez-Bernal, Alejandro Vidal–López. Existence, uniqueness and attractivity properties of positive complete trajectories for non-autonomous reaction-diffusion problems. Discrete & Continuous Dynamical Systems, 2007, 18 (2&3) : 537-567. doi: 10.3934/dcds.2007.18.537 [17] Tomás Caraballo, Antonio M. Márquez-Durán, Rivero Felipe. Asymptotic behaviour of a non-classical and non-autonomous diffusion equation containing some hereditary characteristic. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 1817-1833. doi: 10.3934/dcdsb.2017108 [18] Fatih Bayazit, Ulrich Groh, Rainer Nagel. Floquet representations and asymptotic behavior of periodic evolution families. Discrete & Continuous Dynamical Systems, 2013, 33 (11&12) : 4795-4810. doi: 10.3934/dcds.2013.33.4795 [19] Zhijian Yang, Yanan Li. Criteria on the existence and stability of pullback exponential attractors and their application to non-autonomous kirchhoff wave models. Discrete & Continuous Dynamical Systems, 2018, 38 (5) : 2629-2653. doi: 10.3934/dcds.2018111 [20] Hongbin Chen, Yi Li. Existence, uniqueness, and stability of periodic solutions of an equation of duffing type. Discrete & Continuous Dynamical Systems, 2007, 18 (4) : 793-807. doi: 10.3934/dcds.2007.18.793

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