Differential Variational Inequalities and Differential Nash Games

2010 ◽  
pp. 267-312 ◽  
Author(s):  
Terry L. Friesz
Keyword(s):  
Variational Inequalities ◽  
Nash Games ◽  
Differential Variational Inequalities

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

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 266 ◽  
Author(s):  
Savin Treanţă
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Optimal Control Theory ◽  
Infinite Dimensional ◽  
Nash Games ◽  
New Class ◽  
Set Valued Mappings ◽  
Differential Variational Inequalities ◽  
Theoretical Developments

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.

Existence results of semilinear differential variational inequalities without compactness

Optimization ◽  
2019 ◽  
Vol 68 (5) ◽  
pp. 1017-1035 ◽  
Author(s):  
Liang Lu ◽  
Zhenhai Liu ◽  
Dumitru Motreanu
Keyword(s):  
Variational Inequalities ◽  
Existence Results ◽  
Differential Variational Inequalities

Decay solutions for a class of fractional differential variational inequalities

2015 ◽  
Vol 18 (3) ◽  
Author(s):  
Tran Dinh Ke ◽  
Nguyen Van Loi ◽  
Valeri Obukhovskii
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Fractional Derivatives ◽  
New Class ◽  
Fixed Point Approach ◽  
Fractional Differential ◽  
Differential Variational Inequalities

AbstractOur aim is to study a new class of differential variational inequalities involving fractional derivatives. Using the fixed point approach, the existence of decay solutions to the mentioned problem is proved.

A Class of Delay Differential Variational Inequalities

2016 ◽  
Vol 172 (1) ◽  
pp. 56-69 ◽  
Author(s):  
Xing Wang ◽  
Ya-wei Qi ◽  
Chang-qi Tao ◽  
Yi-bin Xiao
Keyword(s):  
Variational Inequalities ◽  
Delay Differential ◽  
Differential Variational Inequalities
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