Uniqueness and Hyers-Ulam stability results for differential variational inequalities with nonlocal conditions
type: Item
instance of: scholarly article
title: Uniqueness and Hyers-Ulam stability results for differential variational inequalities with nonlocal conditions
zbMATH Open document ID: 1495.34085
author: Nguyen Van Loi
author: Mai Quoc Vu
published in: Differential Equations and Dynamical Systems
publication date: 2022-03-16T00:00:00Z
review text: Let \(H_1,\) \(H_2\) be Hilbert spaces; \(K \subset H_2\) a closed convex subset. The authors study the existence and uniqueness of a solution and the Hyers-Ulam stability of a differential variational inequality of the following form \[ \left\{ \begin{array}{l} x^\prime(t) = f(t,x(t),u(t)), \qquad \quad \;\, t \in I :=[0,T]; \\ \langle v - u(t), g(x(t),u(t))\rangle \geq 0, \quad \forall t \in I, \forall v \in K;\\ u(t) \in K. \qquad \qquad \qquad \qquad \quad \, \forall t \in I, \end{array} \right. \] with the initial condition \[ x(0) = x_0 + h(x), \] where \(f \colon I \times H_1 \times K \to H_1,\) \(g \colon H_1 \times K \to H_2\) and \(h \colon C(I,H_1) \to H_1\) are given maps. As applications, a linear differential complimentarity system and a price control model are presented.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34D10
zbMATH DE Number: 7491023
zbMATH Keywords: differential variational inequality
zbMATH Keywords: Hyers-Ulam stability
zbMATH Keywords: nonlocal condition
zbMATH Keywords: linear complementarity system
zbMATH Keywords: price control
reviewed by: Valerii V. Obukhovskij
MaRDI profile type: Publication
full work available at URL: s12591-018-0429-3
OpenAlex ID: W2886283858
cites work: A stability theory for second-order nonsmooth dynamical systems with application to friction problems.
cites work: On the Ulam-Hyers stability of first order differential systems with nonlocal initial conditions
cites work: Stability of functional equations in single variable.
cites work: On Ulam's type stability for a class of impulsive fractional differential equations with nonlinear integral boundary conditions
cites work: The stability of solutions of linear differential equations
cites work: Lyapunov Stability of Complementarity and Extended Systems
cites work: Q4452862
cites work: Q5706584
cites work: Stability and Instability Matrices for Linear Evolution Variational Inequalities
cites work: Necessary conditions of asymptotic stability for unilateral dynamical systems
cites work: On differential variational inequalities and projected dynamical systems -- equivalence and a stability result
cites work: On a new class of differential variational inequalities and a stability result
cites work: Decay solutions for a class of fractional differential variational inequalities
cites work: Topological methods for some classes of differential variational inequalities
cites work: Condensing multivalued maps and semilinear differential inclusions in Banach spaces
cites work: Ulam type stability for a coupled system of boundary value problems of nonlinear fractional differential equations
cites work: Existence and global bifurcation of periodic solutions to a class of differential variational inequalities
cites work: On two-parameter global bifurcation of periodic solutions to a class of differential variational inequalities
cites work: Nonlocal problem for differential complementarity systems
cites work: Evolutionary problems driven by variational inequalities
cites work: Network economics. A variational inequality approach.
cites work: Stability of some set-valued functional equations
cites work: Differential variational inequalities
cites work: On the Stability of the Linear Mapping in Banach Spaces
cites work: Q3406705
cites work: Uniqueness for index-one differential variational inequalities
cites work: Stability for differential mixed variational inequalities
cites work: Existence and Hyers‐Ulam stability of fractional nonlinear impulsive switched coupled evolution equations
cites work: Hyers-Ulam stability of non-autonomous systems in terms of boundedness of Cauchy problems
Wikidata QID: Q129369505
DOI: 10.1007/S12591-018-0429-3
description: scientific article; zbMATH DE number 7491023