Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (5): 749-764.doi: https://doi.org/10.1007/s10483-017-2191-9

• 论文 • 上一篇    

Existence and stability of solutions to inverse variational inequality problems

Yu HAN1, Nanjing HUANG1, Jue LU1, Yibin XIAO2   

  1. 1. Department of Mathematics, Sichuan University, Chengdu 610064, China;
    2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
  • 收稿日期:2016-06-17 修回日期:2016-09-20 出版日期:2017-05-01 发布日期:2017-05-01
  • 通讯作者: Nanjing HUANG E-mail:nanjinghuang@hotmail.com
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (No. 11671282), the Joint Foundation of the Ministry of Education of China and China Mobile Communication Corporation (No. MCM20150505), the China Postdoctoral Science Foundation (No. 2015T80967), the Applied Basic Project of Sichuan Province (No. 2016JY0170), the Open Foundation of State Key Laboratory of Electronic Thin Films and Integrated Devices (No. KFJJ201611), the Key Program of Education Department of Sichuan Province (No. 16ZA0007), and the Fundamental Research Funds for the Central Universities (No. ZYGX2015J098)

Existence and stability of solutions to inverse variational inequality problems

Yu HAN1, Nanjing HUANG1, Jue LU1, Yibin XIAO2   

  1. 1. Department of Mathematics, Sichuan University, Chengdu 610064, China;
    2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
  • Received:2016-06-17 Revised:2016-09-20 Online:2017-05-01 Published:2017-05-01
  • Contact: Nanjing HUANG E-mail:nanjinghuang@hotmail.com
  • Supported by:

    Project supported by the National Natural Science Foundation of China (No. 11671282), the Joint Foundation of the Ministry of Education of China and China Mobile Communication Corporation (No. MCM20150505), the China Postdoctoral Science Foundation (No. 2015T80967), the Applied Basic Project of Sichuan Province (No. 2016JY0170), the Open Foundation of State Key Laboratory of Electronic Thin Films and Integrated Devices (No. KFJJ201611), the Key Program of Education Department of Sichuan Province (No. 16ZA0007), and the Fundamental Research Funds for the Central Universities (No. ZYGX2015J098)

摘要:

In this paper, two new existence theorems of solutions to inverse variational and quasi-variational inequality problems are proved using the Fan-Knaster-KuratowskiMazurkiewicz (KKM) theorem and the Kakutani-Fan-Glicksberg fixed point theorem. Upper semicontinuity and lower semicontinuity of the solution mapping and the approximate solution mapping to the parametric inverse variational inequality problem are also discussed under some suitable conditions. An application to a road pricing problem is given.

关键词: non-homogeneous cylindrical orthotropic circular plate, transitional region, core-radius ratio, exponential rule, lower semicontinuity, upper semicontinuity, Kakutani-Fan-Glicksberg fixed point theorem, Fan-Knaster-Kuratowski-Mazurkiewicz (KKM) theorem, inverse variational inequality

Abstract:

In this paper, two new existence theorems of solutions to inverse variational and quasi-variational inequality problems are proved using the Fan-Knaster-KuratowskiMazurkiewicz (KKM) theorem and the Kakutani-Fan-Glicksberg fixed point theorem. Upper semicontinuity and lower semicontinuity of the solution mapping and the approximate solution mapping to the parametric inverse variational inequality problem are also discussed under some suitable conditions. An application to a road pricing problem is given.

Key words: non-homogeneous cylindrical orthotropic circular plate, transitional region, core-radius ratio, exponential rule, inverse variational inequality, upper semicontinuity, Kakutani-Fan-Glicksberg fixed point theorem, Fan-Knaster-Kuratowski-Mazurkiewicz (KKM) theorem, lower semicontinuity

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