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

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.

Weak Sharp Type Solutions for Some Variational Integral Inequalities

“…Knowing the implications of variational analysis in multifarious fields, like optimization or control theory, and taking into account some techniques presented by Clarke [8], Treanţȃ [9][10][11][12][13][14][15], Jayswal and Singh [16], Kassay and Rȃdulescu [17], Mititelu and Treanţȃ [18], in this paper, we investigate weak sharp type solutions for a family of variational integral inequalities defined by a convex functional of the multiple integral type. A connection with the sufficiency property associated with the minimum principle is formulated, as well.…”

An Oscillation Criterion of Nonlinear Differential Equations with Advanced Term

“…Oscillation and asymptotic theory, however, has gained particular attention due to its widespread applications in clinical applications, earthquake structures, which involve symmetrical properties; see [3][4][5][6][7][8]. Nowadays, there has been an increasing interest in studying the asymptotic behavior of differential equations, see [9][10][11][12][13][14][15][16][17][18][19][20][21].…”

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

“…Moreover, Migórski and Bai [18] introduced and studied a class of evolution subdifferential inclusions involving history-dependent operators. Also, some evolutionary problems governed by variational inequalities were analyzed in Liu et al [12,13] and Treanţȃ [24].…”