Differential and Integral Inequalities
Theory and Applications
Published on 14. May 2014
335 pages
978-0-08-095564-3 (ISBN)
Description
Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations
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Series
Language
English
Place of publication
Oxford
United States
ISBN-13
978-0-08-095564-3 (9780080955643)
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Schweitzer Classification
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Additional editions
V. Lakshmikantham | S. Leela
Differential and Integral Inequalities: Functional Partial, Abstract and Complex Differential Equations v. 2
Theory and Applications
Book
01/1970
Academic Press
€89.13
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Content
- Front Cover
- Differential and Integral Inequalities
- Copyright Page
- Preface
- Contents
- PART 1: FUNCTIONAL DIFFERENTIAL EQUATIONS
- Chapter 6
- 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
- Chapter 7
- 7.0 Introduction
- 7.1 Stability Criteria
- 7.2 Converse Theorems
- 7.3 Autonomous Systems
- 7.4 Perturbed Systems
- 7.5 Extreme Stability
- 7.6 Almost Periodic Systems
- 7.7 Notes
- Chapter 8
- 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
- PART 2: PARTIAL DIFFERENTIAL EQUATIONS
- Chapter 9
- 9.0 Introduction
- 9.1 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
- 10.1 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 Differential inequalities in Bounded Domains
- 10.7 Lyapunov-Like Functions
- 10.8 Stahility and Boundedness
- 10.9 Conditional Stability and Boundedness
- 10.10 Parabolic Differential Inequalities in Unbounded Domains
- 10.11 Uniqueness
- 10.12 Exterior Boundary-Value Problem and Uniqueness
- 10.13 Notes
- Chapter 11
- 11.0 Introduction
- 11.1 Hyperbolic Diflerential Inequalities
- 11.2 Uniqueness Criteria
- 11.3 Upper Bounds and Error Estimates
- 11.4 Notes
- PART 3: DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES
- Chapter 12
- 12.0 Introduction
- 12.1 Existence
- 12.2 Nonlocal 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
- PART 4: 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
