A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES

doi:10.1007/s10473-021-0111-7

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (1): 187-206.doi: 10.1007/s10473-021-0111-7

A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES

翁云华, 李雪松, 黄南京

Department of Mathematics, Sichuan University, Chengdu 610064, China

收稿日期:2019-11-06 修回日期:2020-08-27 出版日期:2021-02-25 发布日期:2021-04-06
通讯作者: Nanjing HUANG E-mail:nanjinghuang@hotmail.com,njhuang@scu.edu.cn
作者简介:Yunhua WENG,E-mail:yunhuaweng@outlook.com;Xuesong LI,E-mail: xuesongli78@hotmail.com
基金资助:
This work was supported by the National Natural Science Foundation of China (11471230, 11671282).

A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES

Yunhua WENG, Xuesong LI, Nanjing HUANG

Department of Mathematics, Sichuan University, Chengdu 610064, China

Received:2019-11-06 Revised:2020-08-27 Online:2021-02-25 Published:2021-04-06
Contact: Nanjing HUANG E-mail:nanjinghuang@hotmail.com,njhuang@scu.edu.cn
About author:Yunhua WENG,E-mail:yunhuaweng@outlook.com;Xuesong LI,E-mail: xuesongli78@hotmail.com
Supported by:
This work was supported by the National Natural Science Foundation of China (11471230, 11671282).

摘要/Abstract

摘要： This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space. Utilizing the KKM theorem, a result concerned with the upper semicontinuity and measurability of the solution set of a hemi-variational inequality is established. By using a fixed point theorem for a condensing set-valued map, the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions. Finally, an example is presented to illustrate our main results.

关键词: fractional differential variational inequality, fractional nonlinear delay evolution equation, hemi-variational inequality, condensing map, KKM theorem, fixed point theorem

Abstract: This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space. Utilizing the KKM theorem, a result concerned with the upper semicontinuity and measurability of the solution set of a hemi-variational inequality is established. By using a fixed point theorem for a condensing set-valued map, the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions. Finally, an example is presented to illustrate our main results.

Key words: fractional differential variational inequality, fractional nonlinear delay evolution equation, hemi-variational inequality, condensing map, KKM theorem, fixed point theorem

中图分类号:

34A08

翁云华, 李雪松, 黄南京. A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES[J]. 数学物理学报(英文版), 2021, 41(1): 187-206.

Yunhua WENG, Xuesong LI, Nanjing HUANG. A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES[J]. Acta mathematica scientia,Series B, 2021, 41(1): 187-206.

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A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES

A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES

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