Volterra Integral and Differential Equations
Published on 14. May 2014
325 pages
978-0-08-095673-2 (ISBN)
Description
Volterra Integral and Differential Equations
More details
Series
Language
English
Place of publication
San Diego
United States
ISBN-13
978-0-08-095673-2 (9780080956732)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
E-Book
08/2009
2nd Edition
Elsevier
€180.00
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Additional editions
T. A. Burton
Volterra Integral and Differential Equations
Book
01/1983
Academic Press
€97.35
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Content
- Front Cover
- Volterra Integral and Differential Equations
- Copyright Page
- Contents
- Preface
- Chapter 0. Introduction and Overview
- 0.1. Statement of Purpose
- 0.2. An Overview
- Chapter 1. The General Problems
- 1.1. Introduction
- 1.2. Relations between Differential and Integral Equations
- 1.3. A Glance at Initial Conditions and Existence
- 1.4. Building the Intuition
- 1.5. Reducible Equations
- Chapter 2. Linear Equations
- 2.1. Existence Theory
- 2.2. Linear Properties
- 2.3. Convolution and the Laplace Transform
- 2.4. Stability
- 2.5. Liapunov Functionals and Small Kernels
- 2.6. Uniform Asymptotic Stability
- 2.7. Reducible Equations Revisited
- 2.8. The Resolvent
- Chapter 3. Existence Properties
- 3.1. Definitions, Background, and Review
- 3.2. Existence and Uniqueness
- 3.3. Continuation of Solutions
- 3.4. Continuity of Solutions
- Chapter 4. History, Examples, and Motivation
- 4.0. Introduction
- 4.1. Volterra and Mathematical Biology
- 4.2. Renewal Theory
- 4.3. Examples
- Chapter 5. Instability, Stability, and Perturbations
- 5.1. The Matrix ATB + BA
- 5.2. The Scalar Equation
- 5.3. The Vector Equation
- 5.4. Complete Instability
- Chapter 6. Stability and Boundedness
- 6.1. Stability Theory for Ordinary Differential Equations
- 6.2. Construction of Liapunov Functions
- 6.3. A First Integral Liapunov Functional
- 6.4. Nonlinear Considerations and an Annulus Argument
- 6.5. A Functional in the Unstable Case
- Chapter 7. Perturbations
- 7.1. A Converse Theorem Yielding a Perturbation Result
- 7.2. Boundedness under Perturbations
- 7.3. Additive Properties of Functionals
- Chapter 8. Functional Differential Equations
- 8.0. Introduction
- 8.1. Existence and Uniqueness
- 8.2. Asymptotic Stability
- 8.3. Equations with Bounded Delay
- 8.4. Boundedness with Unbounded Delay
- 8.5. Limit Sets
- 8.6. Periodic Solutions
- 8.7. Limit Sets and Unbounded Delays
- References
- Author Index
- Subject Index
