一类微分包含问题的伪概自守解

数学物理学报 ›› 2024, Vol. 44 ›› Issue (6): 1485-1498.

一类微分包含问题的伪概自守解

叶莉¹,刘永建^2,^*(),刘爱民²

¹重庆师范大学数学科学学院重庆 401331
²玉林师范学院, 广西应用数学中心, 广西高校复杂系统优化与大数据处理重点实验室广西玉林 537000

收稿日期:2023-11-06 修回日期:2024-03-25 出版日期:2024-12-26 发布日期:2024-11-22
通讯作者: ^*刘永建, Email: liuyongjianmaths@126.com
作者简介:叶莉, Email:1508793310@qq.com;|刘爱民, Email:254016933@qq.com
基金资助:
国家自然科学基金(12371179)

Pseudo-Almost Automorphic Solutions to A Class of Differential Inclusions

Ye Li¹,Liu Yongjian^2,^*(),Liu Aimin²

¹School of Mathematics Sciences, Chongqing Normal University, Chongqing 401331
²Center for Applied Mathematics of Guangxi, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Guangxi Yulin 537000

Received:2023-11-06 Revised:2024-03-25 Online:2024-12-26 Published:2024-11-22
Supported by:
NSFC(12371179)

摘要/Abstract

摘要：

该文研究一类具有非局部和局部混合初始条件的微分包含问题的伪概自守 $ C^0 $-解. 结合不动点定理、算子半群理论、伪概自守函数的性质, 利用 $ \varepsilon $-离散化技术, 在伪概自守函数空间中直接讨论微分包含 $ C^0 $- 解的存在性.

关键词: 伪概自守 $ C^0 $-解, 微分包含, 混合初始条件

Abstract:

This paper is dedicated to the study of the pseudo-almost automorphic $ C^0 $-solutions to a class of differential inclusion problems which have mixed nonlocal plus local initial conditions. Baseing on the fixed point theorem, theory of operator semigroups, and the properties of pseudo-almost automorphic functions, using $ \varepsilon $-discretisation techniques the existence of $ C^0 $-solutions for differential inclusion is discussed directly in the space which is composed by all pseudo-almost automorphic functions.

Key words: Pseudo almost automorphy $ C^0 $-solution, Differential inclusion, Mix initial conditions

中图分类号:

0175.1

叶莉, 刘永建, 刘爱民. 一类微分包含问题的伪概自守解[J]. 数学物理学报, 2024, 44(6): 1485-1498.

Ye Li, Liu Yongjian, Liu Aimin. Pseudo-Almost Automorphic Solutions to A Class of Differential Inclusions[J]. Acta mathematica scientia,Series A, 2024, 44(6): 1485-1498.

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