The existence and uniqueness problems for some quasi-variational inequalities are studied on the basis of the L∞-estimates for solutions of the variational inequalities and their differences. An implicit obstacle problem is stated by analogy with one quasi-variational inequality studied by Benoussan and Lions (1982) and Vescan (1982) and its unique solvability is proved. Some conclusions are given concerning the uniqueness of solutions for an impulse control problem with bilateral restrictions and for a quasi-variational inequality appearing in dynamic programming.
Variational and quasi-variational inequalities, impulse control, dynamic programming, implicit Signorini problem
MSC 2000: 35J85, 35B50, 58E35, 49J40, 49N25.