Differential and Integral Inequalities - Theory And Applications - Vol 2 Functional Partial, Abstract And Complex Differential Equations

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

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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