On a class of differential quasi-variational-hemivariational inequalities in infinite-dimensional Banach spaces

Abstract

A class of differential quasi-variational-hemivariational inequalities (DQVHI, for short) is studied in this paper. First, based on the Browder's result, KKM theorem and monotonicity arguments, we prove the superpositionally measurability, convexity and strongly-weakly upper semicontinuity for the solution set of a general quasi-variational-hemivariational inequality. Further, by using optimal control theory, measurability of set-valued mappings and the theory of semigroups, we establish that the solution set of (DQVHI) is nonempty and compact. This kind of evolutionary problems incorporates various classes of problems and models.

Weak Sharp Type Solutions for Some Variational Integral Inequalities

“…Knowing the implications of variational analysis in multifarious fields, like optimization or control theory, and taking into account some techniques presented by Clarke [8], Treanţȃ [9][10][11][12][13][14][15], Jayswal and Singh [16], Kassay and Rȃdulescu [17], Mititelu and Treanţȃ [18], in this paper, we investigate weak sharp type solutions for a family of variational integral inequalities defined by a convex functional of the multiple integral type. A connection with the sufficiency property associated with the minimum principle is formulated, as well.…”