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

Savin Treanţă
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Savin Treanţă: Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania

Mathematics, 2021, vol. 9, issue 3, 1-10

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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