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Mathematics
Volume 9
Issue 3
10.3390/math9030266
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Article

On a Class of Differential Variational Inequalities in Infinite-Dimensional Spaces

by
Savin Treanţă
Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Mathematics 2021, 9(3), 266; https://doi.org/10.3390/math9030266
Submission received: 15 January 2021 / Revised: 24 January 2021 / Accepted: 28 January 2021 / Published: 29 January 2021
Versions Notes

Abstract

A new class of differential variational inequalities (DVIs), governed by a variational inequality and an evolution equation formulated in infinite-dimensional spaces, is investigated in this paper. More precisely, based on Browder’s result, optimal control theory, measurability of set-valued mappings and the theory of semigroups, we establish that the solution set of DVI is nonempty and compact. In addition, the theoretical developments are accompanied by an application to differential Nash games.
Keywords: differential variational inequality; existence of solutions; bounded operator; evolutionary problem differential variational inequality; existence of solutions; bounded operator; evolutionary problem

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MDPI and ACS Style

Treanţă, S. On a Class of Differential Variational Inequalities in Infinite-Dimensional Spaces. Mathematics 2021, 9, 266. https://doi.org/10.3390/math9030266

AMA Style

Treanţă S. On a Class of Differential Variational Inequalities in Infinite-Dimensional Spaces. Mathematics. 2021; 9(3):266. https://doi.org/10.3390/math9030266

Chicago/Turabian Style

Treanţă, Savin. 2021. "On a Class of Differential Variational Inequalities in Infinite-Dimensional Spaces" Mathematics 9, no. 3: 266. https://doi.org/10.3390/math9030266

APA Style

Treanţă, S. (2021). On a Class of Differential Variational Inequalities in Infinite-Dimensional Spaces. Mathematics, 9(3), 266. https://doi.org/10.3390/math9030266

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