帮我地道的翻译：The differential variational inequalities ((DVIs), for short) are useful for the study of models involving both dynamics and constraints in the form of in￾equalities. They arise in many applications: electrical circuits with ideal diodes, Coulomb friction problems for contacting bodies, economical dynamics, dynamic traffic networks. Pang and Stewart [26], [27] established the existence, unique￾ness, and Lipschitz dependence of solutions subject to boundary conditions for (DVIs) in finite dimensional spaces. Han and Pang investigated a class of dif￾ferential quasi-variational inequalities in [11], and Li, Huang and O’Regan [18] studied a class of differential mixed variational inequalities in finite dimensional Well-Posedness of Differential Mixed Quasi-Variational-Inequalities 137 spaces. Gwinner [8] obtained an equivalence result between (DVIs) and projected dynamical systems. In [9] he also proved a stability property for (DVIs) by using the monotonicity method of Browder and Minty, and Mosco set convergence. Chen and Wang [4] studied dynamic Nash equilibrium problems which have the formulation of differential mixed quasi-variational inequalities. Elastoplastic contact problems can also be incorporated into (DMQVIs) formulation because general dynamic processes in the nonsmooth unilateral contact problems are governed by quasi-variational inequalities. A numerical study for nonsmooth contact problems with Tresca friction can be found in [10], Liu, Loi and Obukhovskii [19] studied the existence and global bifurcation for periodic solutions of a class of (DVIs) by using the topological degree theory for multivalued maps and the method of guiding functions. For more details about (DVIs) we refer to [3], [30], [12], [22]–[21].