A class of differential inverse quasi-variational inequalities in finite dimensional spaces

Volume 10, Issue 8, pp 4532--4543 http://dx.doi.org/10.22436/jnsa.010.08.45

Publication Date: August 31, 2017 Submission Date: July 13, 2017

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Authors

Wei Li - Geomathematics Key Laboratory of Sichuan Province, Chengdu University of Technology, Chengdu, Sichuan, 610059, P. R. China. - State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu, Sichuan, 610059, P. R. China. Yi-Bin Xiao - School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731, P. R. China. Nan-Jing Huang - Department of Mathematics, Sichuan University, Chengdu, 610064, P. R. China. Yeol Je Cho - Department of Mathematics Education and the RINS, Gyeongsang National University, Jinju 660-701, Korea. - Center for General Education, China Medical University, Taichung 40402, Taiwan.

Abstract

In this paper, we introduce and study a class of differential inverse quasi-variational inequalities in finite dimensional Euclidean spaces, which are closely related to the differential variational inequalities. By using two important theorems on differential inclusions, we first prove some existence theorems for Carathéodory weak solutions of the differential inverse quasi-variational inequality considered. Then, with the Euler computation method, we construct an Euler time-dependent scheme for solving the differential inverse quasi-variational inequality and prove a convergence result on the Euler time-dependent scheme constructed.

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Keywords

• Differential inverse quasi-variational inequality
• Carathéodory weak solution
• Euler time-stepping scheme.

MSC

•  49J40
•  35D30
•  40A05

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