Banach空间中强伪单调变分不等式解的唯一性和稳定性  

Uniqueness and Stability of the Solution for Strongly Pseudomonotone Variational Inequalities in Banach Spaces

作　　者：唐国吉 李延恕 TANG Guoji;LI Yanshu(School of Science, Guangxi University for Nationalities, Nanning, Guangxi, 530006, P. R. 2. Guangxi Colleges and Universities Key Laboratory of Mathematical and Statistical Model, Guangxi, 541004, P. R. China)

机构地区：[1]广西民族大学理学院,南宁广西530006 [2]广西高校数学与统计模型重点实验室,桂林广西541004

出　　处：《数学进展》2018年第3期455-462,共8页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.11561008);广西自然科学基金(No.2014GXNSFAA118006);广西高校千名中青年骨干教师培育计划(桂教人(2018)18号);广西八桂学者专项(No.WBS-2014-04);广西高校数学与统计模型重点实验室开放基金课题(No.2016GXKLMS012)

摘　　要：在自反Banach空间中证明强伪单调变分不等式解的存在唯一性定理.在此基础上研究扰动变分不等式解的稳定性.此外,也在有限维空间中得到了强拟单调变分不等式解的存在性定理.In this paper, we prove an existence and unique theorem of the solution for strongly pseudomonotone variational inequalities in reflexive Banach spaces. Based on this result,we investigate the stability behavior of the perturbed variational inequalities. Moreover, we obtain an existence theorem of solutions for strongly quasimonotone variational inequalities in finite dimensional spaces.

关 键 词：变分不等式 强伪单调 强拟单调 存在唯一性 稳定性 

分 类 号：O221.2[理学—运筹学与控制论]