自反Banach空间中广义混合拟变分不等式解的存在唯一性OA
Existence and Uniqueness of Solutions for Generalized Mixed Quasi-variational Inequalities in Reflexive Banach Spaces
基于Brezis伪单调集值映射与双函数的相关性质,本文在自反Banach空间中,利用序列逼近方法探讨广义混合拟变分不等式(简记为GMQVI)与其罚问题、正则化罚问题之间的关系,在弱紧集中给出了一个GMQVI解的存在性定理;在无界情况下,构造强制性条件,得到了一个GMQVI解的存在性定理;进而在存在性基础上,得出GMQVI解的唯一性定理.
Using on the properties of Brezis pseudomonotone set-valued mappings and bifunctions,this paper employs approximation method to explore the relationships among the generalized mixed quasi-variational inequality(GMQVI),its penalty problem,and the regularized penalty problem in reflexive Banach spaces.An existence theorem for the solutions to GMQVI is given on a weakly compact set.In the unbounded case,by constructing the coercivity condition,an existence theorem for the solutions to GMQVI is obtained.Furthermore,based on these existence results,a uniqueness theorem for the solutions to GMQVI is derived.
徐安慧;林惠玲
福建师范大学数学与统计学院,福建 福州 350117福建师范大学数学与统计学院,福建 福州 350117
数理科学
广义混合拟变分不等式Brezis伪单调序列逼近方法罚问题
Generalized mixed quasi-variational inequalityBrezis pseudomonotoneApproxima-tion methodPenalty problem
《应用数学》 2026 (2)
444-456,13
福建省自然科学基金(2021J01654)
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