广义向量拟似变分不等式的通有稳定性和本质连通区  

The Stability and the Existence of Essential Components of the Solution Sets for generalized vector quasi-variational-like inequalities

作　　者：李盛强[1] 

机构地区：[1]重庆大学数学与统计学院,重庆401331

出　　处：《重庆理工大学学报（自然科学）》2012年第11期115-122,共8页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学基金资助项目(11171362)

摘　　要：利用广义拟似变分不等式解集的存在性定理,构造了一个满足广义拟似变分不等式问题存在性定理的函数空间M,证明了函数空间M的完备性,并讨论了在M中该问题解集的稳定性,得到了M映射到解集的映射是usco映射的结论。引入解集本质连通区的概念,并证明每一个广义拟似变分不等式的解集至少存在一个本质连通区。研究了解集本质连通区的稳定性。This paper applies the existence theorem of the solution for generalized vector quasi-variational-like inequalities（GVQVLI） to construct a functional space M satisfying the existence theorem,proves the completeness of functional space M,and also discusses the stability of the solution sets for generalized vector quasi-variational-like inequalities,and obtains an important conclusion that the mapping which maps the M to the solution sets is usco.Then,this paper introduces the notion of essential connected components for the solution sets and proves that every solution set for generalized vector quasi-variational-like inequalities has at least one essential connected components.Finally,we study the stability of essential connected components for the solution sets.

关 键 词：广义拟似变分不等式 本质连通区 usco映射 解集稳定性 

分 类 号：O178[理学—数学]