Existence and stability for a generalized differential mixed quasi-variational inequality

2018 ◽  
Vol 34 (3) ◽  
pp. 347-354
Author(s):  
WEI LI ◽  
◽  
YI-BIN XIAO ◽  
XING WANG ◽  
JUN FENG ◽  
...  
Keyword(s):  
Weak Solution ◽  
Variational Inequality ◽  
Existence Result ◽  
Upper Semicontinuity ◽  
Measurable Selection ◽  
Existence And Stability ◽  
Quasi Variational Inequality ◽  
Carathéodory Weak Solution ◽  
Generalized Differential ◽  
Stability Results

In the present paper, we investigate a generalized differential mixed quasi-variational inequality consisting of a system of an ordinary differential equation and a generalized mixed quasi-variational inequality. By using an important result concerning the measurable selection, we prove the existence of Caratheodory weak solution to ´ the generalized differential mixed quasi-variational inequality. Then, with the existence result, we establish two stability results for the generalized differential mixed quasi-variational inequality under different conditions, i.e., upper semicontinuity and lower semicontinuity of the Caratheodory weak solution with respect to the ´ parameter, which is a perturbation of some mappings in the generalized mixed quasi-variational inequality.

scholarly journals A generalised quasi-variational inequality without upper semicontinuity

1996 ◽  
Vol 54 (2) ◽  
pp. 247-254 ◽  
Author(s):  
Paolo Cubiotti ◽  
Xian-Zhi Yuan
Keyword(s):  
Variational Inequality ◽  
Convex Subset ◽  
Existence Result ◽  
Upper Semicontinuity ◽  
Nonempty Closed Convex Subset ◽  
Positive Answer ◽  
Upper Semicontinuous ◽  
Quasi Variational Inequality ◽  
General Existence ◽  
Image Position

In this note we deal with the following problem: given a nonempty closed convex subset X of Rn and two multifunctions Γ : X → 2X and , to find ( such thatWe prove a very general existence result where neither Γ nor Φ are assumed to be upper semicontinuous. In particular, our result give a positive answer to an open problem raised by the first author recently.

scholarly journals Existence and Stability of Solutions for Hadamard-Stieltjes Fractional Integral Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Saïd Abbas ◽  
Eman Alaidarous ◽  
Mouffak Benchohra ◽  
Juan J. Nieto
Keyword(s):  
Integral Equations ◽  
Fractional Integral ◽  
Existence Result ◽  
Existence Results ◽  
Stieltjes Integral ◽  
Ulam Stability ◽  
Stability Of Solutions ◽  
Existence And Stability ◽  
Stability Results ◽  
Rassias Stability

We give some existence results and Ulam stability results for a class of Hadamard-Stieltjes integral equations. We present two results: the first one is an existence result based on Schauder’s fixed point theorem and the second one is about the generalized Ulam-Hyers-Rassias stability.

scholarly journals Existence for Competitive Equilibrium by Means of Generalized Quasivariational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
I. Benedetti ◽  
M. B. Donato ◽  
M. Milasi
Keyword(s):  
Variational Inequality ◽  
Equilibrium Model ◽  
Variational Approach ◽  
Existence Result ◽  
Competitive Equilibrium ◽  
Quasivariational Inequalities ◽  
Existence Of Equilibrium ◽  
Upper Semicontinuous ◽  
Generalized Quasivariational Inequalities ◽  
Quasi Variational Inequality

A competitive economic equilibrium model integrated with exchange, consumption, and production is considered. Our goal is to give an existence result when the utility functions are concave, proper, and upper semicontinuous. To this aim we are able to characterize the equilibrium by means of a suitable generalized quasi-variational inequality; then we give the existence of equilibrium by using the variational approach.

scholarly journals Modified duality methods for solving an elastic crack problem with Coulomb friction on the crack faces

2020 ◽  
Vol 10 (1) ◽  
pp. 276-282
Author(s):  
Robert V. Namm ◽  
Georgiy I. Tsoy
Keyword(s):  
Variational Inequality ◽  
Elastic Body ◽  
Approximation Method ◽  
Coulomb Friction ◽  
Auxiliary Problem ◽  
Crack Problem ◽  
Successive Approximation Method ◽  
Elastic Crack ◽  
Quasi Variational Inequality ◽  
Crack Faces

AbstractWe consider an equilibrium problem for an elastic body with a crack, on the faces of which unilateral non-penetration conditions and Coulomb friction are realized. This problem can be formulated as quasi-variational inequality. To solve it, the successive approximation method is applied. On each outer step of this method, we solve an auxiliary problem with given friction. We solve the auxiliary problem by using modified Lagrange functionals. Numerical results are presented.

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