Differential and integral inequalities: theory and applications PART B

Differential and integral inequalities 

theory and applications PART B: 

Functional, partial, abstract, and complex differential equations, Volume 55B

 (Mathematics in Science and Engineering) (v. 2)

Product Details

V. LAKSHMIKANTHAM and S. LEELA 
University of Rhode Island 
Kingston, Rhode Island 

• Hardcover: 319 pages
• Publisher: Academic Press (February 11, 1969)
• Language: English
• ISBN-10: 0124341020
• ISBN-13: 978-0124341029

Contents 
FUNCTIONAL DIFFERENTIAL EQUATIONS 
6.0. Introduction 
6.1. Existence 
6.2. Approximate Solutions and Uniqueness 
6.3. Upper Bounds 
6.4. Dependence on Initial Values and Parameters 
6.5. Stability Criteria 
6.6. Asymptotic Behavior 
6.7. A Topological Principle 
6.8. Systems with Repulsive Forces 
6.9. Functional Differential Inequalities 
6.10. Notes 
7.0. Introduction 
7.1. Stability Criteria 
7.2. Converse Theoreins 
7.3. Autonomous Systems 
7.4. Perturbed Systems 
7.5. Extreme Stability 
7.6. Almost Periodic Systems 
7.7. Notes 
8.0. Introduction 
8.1. Basic Comparison Theorems 
8.2. Stability Criteria 
8.3. Perturbed Systems 
8.4. An Estimate of Time Lag 
8.5. Eventual Stability 
8.6. Asymptotic Behavior 
8.7. Notes 
PARTIAL DIFFERENTIAL EQUATIONS 
Chapter 9. 9.0. Introduction 
9. I . Partial Differential Inequalities of First Order 
9.2. Comparison Theorems 
9.3. Upper Bounds 
9.4. Approximate Solutions and Uniqueness 
9.5. Systems of Partial Differential Inequalities of First Order 
9.6. Lyapunov-Like Function 
9.7. Notes 
Chapter 10. 10.0. lntroduction 
10. I . Parabolic Differential Inequaliies in Bounded Domains 
10.2. Comparison Theorems 
10.3. Bounds, Under and Over Functions 
10.4. Approximate Solutions and Uniqueness 
10.5. Stability of Steady-State Solutions 
10.6. Systems of Parabolic Diffcrential inequalities in Bounded 
10.7. Lyapunov-Like Functions 
10.8. Stahility and Boundedness 
10.9. Conditional Stahility and Boundedness 
Domains 
10.10. Parabolic Differential Inequalities in Unbounded Domains 
10.11. Uniqueness 
10.12. Exterior Boundary-Value Problem and Uniqueness 
10.13. Notes 
Chapter 11. I 1.0. Introduction 
1 1.1, Hyperbolic Diflerential Inequalities 
1 1.2. Uniqueness Criteria 
11.3. Upper Bounds and Error Estimates 
11.4. Notes 
DIFFERENTIAL EQUATIONS IN ABSTRACT 
SPACES 
Chapter 12. 12.0. Introduction 
12. I . Existence 
12.2. Norilocal Existence 
12.3. Uniqueness 
12.4. Continuous Dependence and the Method of Averaging 
12.5. Existence (continued) 
12.6. Approximate Solutions and Uniqueness 
12.7. Chaplygin’s Method 
12.8. Asymptotic Behavior 
12.9. Lyapunov Function and Comparison Theorems 
12.10. Stability and Boundedness 
12.11. Notes 
COMPLEX DIFFERENTIAL EQUATIONS
Chapter 13. 13.0. Introduction
13.1. Existence, Approximate Solutions, and Uniqueness
13.2. Singularity-Free Regions and Growth Estimates
13.3. Componentwise Bounds
13.4. Lyapunov-like Functions and Comparison Theorems
13.5. Notes
Bibliography
Author Index
Subject Index
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