scholarly journals On homotopy invariance of the solvability of nonlinear variational inequalities

1985 ◽  
Vol 8 (3) ◽  
pp. 277-284 ◽  
Author(s):  
Norimichi Hirano
Keyword(s):  
Variational Inequalities ◽  
Homotopy Invariance

scholarly journals About One Class of Operators Inclusions

2015 ◽  
Vol 19 (3) ◽  
pp. 63-72
Author(s):  
N. A. Demyankov ◽  
V. S. Klimov
Keyword(s):  
Variational Inequalities ◽  
Bounded Operator ◽  
Multivalued Mappings ◽  
Homotopy Invariance ◽  
Operator Inclusion ◽  
Reflexive Space ◽  
Multivalued Operators ◽  
Set Up ◽  
Monotone Type

The operator inclusion 0 ∈ A(x)+N(x) is studied. The main results refer to the case, when A – a bounded operator of monotone type from a reflexive space into conjugate to it, N – a conevalued operator. No solution criterion of the viewed inclusion is set up. Integer characteristics of multivalued mappings with homotopy invariance and additivity are introduced. Application to the theory of variational inequalities with multivalued operators is identified.

Variational and Quasi-Variational Inequalities in Mechanics

2007 ◽  
Author(s):  
Alexander S. Kravchuk ◽  
Pekka J. Neittaanmäki
Keyword(s):  
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.

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