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

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PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

Zhenhai Liu1,2,*, Nikolaos S. Papageorgiou3   

  1. 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 Liu1,2,*, Nikolaos S. Papageorgiou3   

  1. 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: 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