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

Savin Treanţă

doi:10.3934/eect.2021027

Article Contents

2022, Volume 11, Issue 3: 827-836. Doi: 10.3934/eect.2021027

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

Savin Treanţă^,

Department of Applied Mathematics, Faculty of Applied Sciences, University Politehnica of Bucharest, Bucharest 060042, Romania

^* Corresponding author: Savin Treanţă
^* Corresponding author: Savin Treanţă

Received: October 31, 2020

Revised: February 28, 2021

Published: June 2022

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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.

Keywords:

Evolutionary computations,
differential quasi-variational-hemivariational inequality,
existence of solutions,
bounded operator,
evolutionary problem.

Mathematics Subject Classification: Primary: 49J40; Secondary: 47J20.

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