数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (5): 1569-1578.doi: 10.1007/s10473-021-0510-9

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THE NONEMPTINESS AND COMPACTNESS OF MILD SOLUTION SETS FOR RIEMANN-LIOUVILLE FRACTIONAL DELAY DIFFERENTIAL VARIATIONAL INEQUALITIES

蒋宜蓉1, 魏周超2, 卢景苹1   

  1. 1. College of Science, Guilin University of Technology, Guilin 541004, China;
    2. School of Mathematics and Physics, China University of Geosciences(Wuhan), Wuhan 430074, China
  • 收稿日期:2020-01-10 修回日期:2021-04-11 出版日期:2021-10-25 发布日期:2021-10-21
  • 通讯作者: Jingping LU E-mail:lujingbaby520@163.com
  • 作者简介:Yirong JIANG,E-mail:jiangyirong996@126.com;Zhouchao WEI,E-mail:weizhouchao@163.com
  • 基金资助:
    This work was supported by the National Natural Science Foundation of China (11772306), Natural Science Foundation of Guangxi Province (2018GXNSFAA281021), Guangxi Science and Technology Base Foundation (AD20159017), the Foundation of Guilin University of Technology (GUTQDJJ2017062) and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUGGC05).

THE NONEMPTINESS AND COMPACTNESS OF MILD SOLUTION SETS FOR RIEMANN-LIOUVILLE FRACTIONAL DELAY DIFFERENTIAL VARIATIONAL INEQUALITIES

Yirong JIANG1, Zhouchao WEI2, Jingping LU1   

  1. 1. College of Science, Guilin University of Technology, Guilin 541004, China;
    2. School of Mathematics and Physics, China University of Geosciences(Wuhan), Wuhan 430074, China
  • Received:2020-01-10 Revised:2021-04-11 Online:2021-10-25 Published:2021-10-21
  • Contact: Jingping LU E-mail:lujingbaby520@163.com
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (11772306), Natural Science Foundation of Guangxi Province (2018GXNSFAA281021), Guangxi Science and Technology Base Foundation (AD20159017), the Foundation of Guilin University of Technology (GUTQDJJ2017062) and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUGGC05).

摘要: This paper investigates the nonemptiness and compactness of the mild solution set for a class of Riemann-Liouville fractional delay differential variational inequalities, which are formulated by a Riemann-Liouville fractional delay evolution equation and a variational inequality. Our approach is based on the resolvent technique and a generalization of strongly continuous semigroups combined with Schauder's fixed point theorem.

关键词: differential variational inequality, Riemann-Liouville fractional delay evolution equation, resolvent, Schauder's fixed point theorem

Abstract: This paper investigates the nonemptiness and compactness of the mild solution set for a class of Riemann-Liouville fractional delay differential variational inequalities, which are formulated by a Riemann-Liouville fractional delay evolution equation and a variational inequality. Our approach is based on the resolvent technique and a generalization of strongly continuous semigroups combined with Schauder's fixed point theorem.

Key words: differential variational inequality, Riemann-Liouville fractional delay evolution equation, resolvent, Schauder's fixed point theorem

中图分类号: 

  • 34A08