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

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  • Savin Treanţă

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania)

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.

Suggested Citation

  • Savin Treanţă, 2021. "On a Class of Differential Variational Inequalities in Infinite-Dimensional Spaces," Mathematics, MDPI, vol. 9(3), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:266-:d:489258
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    References listed on IDEAS

    as
    1. Xing Wang & Nan-jing Huang, 2014. "A Class of Differential Vector Variational Inequalities in Finite Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 633-648, August.
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