Article
Licensed
Unlicensed
Requires Authentication
On the Uniqueness of Solutions of Some Quasi-Variational Inequalities from Control Theory
-
A. Gachechiladze
Published/Copyright:
March 4, 2010
Abstract
The existence and uniqueness problems for some quasi-variational inequalities are studied on the basis of the L∞-estimates for solutions of the variational inequalities and their differences. An implicit obstacle problem is stated by analogy with one quasi-variational inequality studied by Benoussan and Lions (Méthodes Mathématiques de l'Informatique 11: 1982) and Vescan (1982) and its unique solvability is proved. Some conclusions are given concerning the uniqueness of solutions for an impulse control problem with bilateral restrictions and for a quasi-variational inequality appearing in dynamic programming.
Key words and phrases:: Variational and quasi-variational inequalities; impulse control; dynamic programming; implicit Signorini problem
Received: 2003-01-04
Revised: 2004-03-12
Published Online: 2010-03-04
Published in Print: 2004-June
© Heldermann Verlag
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Maximal Subgroups of Some Classes of Semigroups of Binary Relations
- Additive Surjections Preserving Rank One and Applications
- Some Families of Generating Functions for the Bessel and Related Functions
- On the Uniqueness of Solutions of Some Quasi-Variational Inequalities from Control Theory
- The Existence of Solutions for a Semilinear Abstract Dirichlet Problem
- Noncommutative Symplectic Foliation, Bott Connection and Phase Space Reduction
- Karoubi–Villamayor K-Theory, Weakly Stable C*-Categoroids, and KK-Theory
- On Absolutely Nonmeasurable Additive Functions
- On Higher Order Functional Differential Equations with Property A
- On the Behavior of Solutions of Linear Neutral Integrodifferential Equations with Unbounded Delay
- Invariant Regions and Global Existence of Solutions for Reaction-Diffusion Systems with a Full Matrix of Diffusion Coefficients and Nonhomogeneous Boundary Conditions
- A Sharp Endpoint Estimate for a Multilinear Littlewood–Paley Operator
- On an Initial-Boundary Value Problem for a Fourth Order Composite Equation with Bilaplacian
- An Application of Independent Families of Sets to the Measure Extension Problem
- Oscillation Results for Second Order Self-Adjoint Matrix Differential Systems
Keywords for this article
Variational and quasi-variational inequalities;
impulse control;
dynamic programming;
implicit Signorini problem
Articles in the same Issue
- Maximal Subgroups of Some Classes of Semigroups of Binary Relations
- Additive Surjections Preserving Rank One and Applications
- Some Families of Generating Functions for the Bessel and Related Functions
- On the Uniqueness of Solutions of Some Quasi-Variational Inequalities from Control Theory
- The Existence of Solutions for a Semilinear Abstract Dirichlet Problem
- Noncommutative Symplectic Foliation, Bott Connection and Phase Space Reduction
- Karoubi–Villamayor K-Theory, Weakly Stable C*-Categoroids, and KK-Theory
- On Absolutely Nonmeasurable Additive Functions
- On Higher Order Functional Differential Equations with Property A
- On the Behavior of Solutions of Linear Neutral Integrodifferential Equations with Unbounded Delay
- Invariant Regions and Global Existence of Solutions for Reaction-Diffusion Systems with a Full Matrix of Diffusion Coefficients and Nonhomogeneous Boundary Conditions
- A Sharp Endpoint Estimate for a Multilinear Littlewood–Paley Operator
- On an Initial-Boundary Value Problem for a Fourth Order Composite Equation with Bilaplacian
- An Application of Independent Families of Sets to the Measure Extension Problem
- Oscillation Results for Second Order Self-Adjoint Matrix Differential Systems
