A Class of Multivalued Quasi-Variational Inequalities with Applications

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 r...

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Bibliographic Details
Published in:Applied mathematics & optimization Vol. 87; no. 2; p. 32
Main Authors: Migórski, Stanislaw, Bai, Yunru, Dudek, Sylwia
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2023
Springer Nature B.V
Subjects:
Applied mathematics
Banach spaces
Calculus of Variations and Optimal Control; Optimization
Control
Inequalities
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimization
Perturbation
Science
Simulation
Systems Theory
Theoretical
Hemivariational inequality
Variational inequality
Nonsmooth contact problem
49J40
Clarke subgradient
76A05
Mosco convergence
76M30
P35J87
Kuratowski convergence
Fixed point
ISSN:0095-4616, 1432-0606
Online Access:Get full text
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Summary: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.
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ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-022-09941-5