PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

doi:10.1007/s10473-024-0406-6

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (4): 1280-1300.doi: 10.1007/s10473-024-0406-6

PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

Zhenhai Liu^1,2,*, Nikolaos S. Papageorgiou³

1. Center for Applied Mathematics of Guangxi, Yulin Normal University, Yulin 537000, China;
2. Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation, College of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, China;
3. Department of Mathematics, National Technical University, Zografou Campus, 15780 Athens, Greece

收稿日期:2023-03-23 出版日期:2024-08-25 发布日期:2024-08-30

PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

Zhenhai Liu^1,2,*, Nikolaos S. Papageorgiou³

1. Center for Applied Mathematics of Guangxi, Yulin Normal University, Yulin 537000, China;
2. Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation, College of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, China;
3. Department of Mathematics, National Technical University, Zografou Campus, 15780 Athens, Greece

Received:2023-03-23 Online:2024-08-25 Published:2024-08-30
Contact: *E-mail: zhhliu@hotmail.com
About author:E-mail: npapg@math.ntua.gr
Supported by:
The work was supported by the NSFC (12071413), the Guangxi Natural Science Foundation (2023GXNSFAA026085) and the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No. 823731 CONMECH.

摘要/Abstract

摘要： We consider a first order periodic system in $\mathbb R^N$, involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation. We prove the existence theorems for both the convex and nonconvex problems. We also show the existence of extremal periodic solutions and provide a strong relaxation theorem. Finally, we provide an application to nonlinear periodic control systems.

关键词: periodic boundary condition, time-dependent maximal monotone operator, convex and nonconvex problems, extremal solutions, strong relaxation

Abstract: We consider a first order periodic system in $\mathbb R^N$, involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation. We prove the existence theorems for both the convex and nonconvex problems. We also show the existence of extremal periodic solutions and provide a strong relaxation theorem. Finally, we provide an application to nonlinear periodic control systems.

Key words: periodic boundary condition, time-dependent maximal monotone operator, convex and nonconvex problems, extremal solutions, strong relaxation

中图分类号:

34A34

Zhenhai Liu, Nikolaos S. Papageorgiou. PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS[J]. 数学物理学报(英文版), 2024, 44(4): 1280-1300.

Zhenhai Liu, Nikolaos S. Papageorgiou. PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS[J]. Acta mathematica scientia,Series B, 2024, 44(4): 1280-1300.

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PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

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