Overview

This monograph is devoted to the development of a unified approach for studying differential inclusions in a Banach space with non-convex right-hand side, a new branch of the classical theory of ordinary differential equations. Differential inclusions are now a mature field of mathematical activity, with their own methods, techniques, and applications, which range from economics to physics and biology. The current approach relies on ideas and methods from modern functional analysis, general topology, the theory of multifunctions, and continuous selectors. Audience: This volume will be of interest to researchers and postgraduate student whose work involves differential equations, functional analysis, topology, and the theory of set-valued functions.

Full Product Details

Author:   Alexander Tolstonogov
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of hardcover 1st ed. 2000
Volume:   524
Dimensions:   Width: 17.00cm , Height: 1.70cm , Length: 24.40cm
Weight:   0.555kg
ISBN:  

9789048155804

ISBN 10:   9048155800
Pages:   302
Publication Date:   06 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1. Multi-Valued Differential Equation Generated by A Differential Inclusion.- 1. Background of the theory of measurable multi-valued mappings and differential inequalities.- 2. Existence of local solutions of a multi-valued differential equation with conditions of compactness type.- 3. Existence of local solutions of a multi-valued differential equation. Comparison theorems.- 4. Global solutions of a multi-valued differential equation.- 5. Existence theorems of solutions of the multi-valued operator equation.- 6. Notes and Remarks.- 2. Differential Inclusions. Existence of Solutions.- 1. Types of solutions of a differential inclusion.- 2. Semicontinuous multi-functions.- 3. Strongly measurable selectors of multi-functions.- 4. Continuous selectors of multi-functions with decomposable values.- 5. Continuous selectors of a multi-valued mappings generated by differential inclusions with non-convex right hand side.- 6. Multi-valued selectors of a multi-valued mapping generated by a differential inclusion.- 7. Existence of solutions of a differential inclusion with nonconvex right hand side continuous in x.- 8. Existence of the solution of a differential inclusion with right hand side semicontinuous in x.- 9. Notes and Remarks.- 3. Properties of Solutions.- 1. Auxiliary results.- 2. The density theorems.- 3. The co-density theorems.- 4. Compactness of the set of solutions.- 5. Dependence of the set of solutions on initial conditions and parameters.- 6. Connectedness of the set of solutions.- 7. Notes and remarks.- 4. Integral Funnel of the Differential Inclusion.- 1. Auxiliary lemmas.- 2. The equation of the integral funnel.- 3. Solutions of the equation of the integral funnel.- 4. Properties of solutions of the equation of the integral funnel.- 5. Properties of the integralfunnel.- 6. Extreme points of the set of solutions of a linear differential inclusion.- 7. Notes and Remarks.- 5. Inclusions with Non-Compact Right Hand Side.- 1. Continuous selectors of fixed point sets of multi-functions with decomposable values.- 2. Properties of the multi-valued Nemytskii operator.- 3. Continuous selectors of fixed point sets of the multi-valued Nemytskii operator.- 4. Existence and properties of solution sets of differential inclusion.- 5. Notes and Remarks.- Appendices.- A—.- 1. Non-convex problem of calculus of variations.- 2. Existence of optimal control without assumptions of convexity.- 3. Extension in continuity of multi-valued mappings.- 4. Equivalence of differential inclusions and control systems.- References.- Symbols.

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