A Class of Multivalued Quasi-Variational Inequalities with Applications - Migórski, Stanislaw; Bai, Yunru; Dudek, Sylwia (Applied mathematics & optimization, 2023)
In this paper we deal with a class of nonlinear quasi-variational inequalities involving a set-valued map and a constraint set. First, we prove that the set of weak solutions of the inequality is nonempty, weakly compact and upper semicontinuous with respect to perturbations in the data. Then, the results are applied to a quasi variational-hemivariational inequality of elliptic kind. Finally, as an illustrative applications we examine a mathematical model of a nonsmooth static frictional unilateral contact problem for ideally locking materials in nonlinear elasticity.