Banach空间中一类微分逆变分不等式解的存在性、唯一性及稳定性  

Existence,Uniqueness and Stability of Solutions of a Class of Differential Inverse Inequalities in Banach Spaces

作　　者：谭惠心 徐可 朱新月 李为 冯俊[1] TAN Huixin;XU Ke;ZHU Xinyue;LI Wei;FENG Jun(College of Mathematics and Physics,Chengdu University of Technology,Chengdu 610059,Sichuan)

机构地区：[1]成都理工大学数理学院,四川成都610059

出　　处：《四川师范大学学报（自然科学版）》2024年第1期74-81,共8页Journal of Sichuan Normal University（Natural Science）

基　　金：四川省自然科学基金青年基金(2023NSFSC1358);四川省科技厅项目(2021YJ0351);数学地质四川省重点实验室开放基金(SCSXDZ2021YB06)。

摘　　要：在实自反Banach空间中证明了一类微分逆变分不等式解的存在性、唯一性及稳定性.首先,通过KKM定理证明了逆变分不等式解的存在性,进一步在映射满足单调plus假设下得到逆变分不等式解的唯一性;其次,将微分逆变分不等式问题转化为一个发展方程,利用算子半群的相关知识得到微分逆变分不等式mild解的存在性及其唯一性;再次,考虑了微分逆变分不等式受参数扰动时,微分逆变分不等式的mild解的稳定性.最后,举出一个数值例子,绘制轨线图像,验证定理结论.In this paper,we consider the existence,uniqueness and stability of the solution for a class of differential inverse variational inequality in finite dimensional spaces.Firstly,by applying KKM theorem,we prove the existence of the solution for inverse variational inequality and obtain the uniqueness of the solution for inverse variational inequality under some conditions.Secondly,the existence and uniqueness of mild solutions for the differential inverse variational inequality are established.Finally,a general stability result for the differential inverse variational inequality is provided in the case the perturbed parameter is involved in the nonlinear mapping.Finally,a numerical example is provided to illustrate our main results.

关 键 词：KKM定理 微分逆变分不等式 自然拟凸函数 发展方程 

分 类 号：O224[理学—运筹学与控制论]