Differential quasi-variational inequalities in finite dimensional spaces

Abstract

In this paper, we introduce and study a new class of differential quasi-variational inequalities in finite dimensional Euclidean spaces. First, we prove existence theorems for Carathéodory weak solutions of the differential quasi-variational inequalities under various conditions. Furthermore, we establish a convergence result on Euler time-dependent procedure for solving the initial-value differential set-valued variational inequalities.

Keywords:

• Differential quasi-variational inequality
• Carathéodory weak solution
• existence
• linear growth
• Euler time-stepping procedure

Acknowledgments

The authors are grateful to the editor and the referees for their valuable comments and suggestions.

Additional information

Funding

This work was supported by the Key Program of NSFC [grant number 70831005] and the National Natural Science Foundation of China [grant number 11171237].