Volterra Integral and Differential Equations

T.A. Burton (Eds.)9780080459554, 9780444517869, 0444517863

Most mathematicians, engineers, and many other scientists are well-acquainted with theory and application of ordinary differential equations. This book seeks to present Volterra integral and functional differential equations in that same framwork, allowing the readers to parlay their knowledge of ordinary differential equations into theory and application of the more general problems. Thus, the presentation starts slowly with very familiar concepts and shows how these are generalized in a natural way to problems involving a memory. Liapunov’s direct method is gently introduced and applied to many particular examples in ordinary differential equations, Volterra integro-differential equations, and functional differential equations.
By Chapter 7 the momentum has built until we are looking at problems on the frontier. Chapter 7 is entirely new, dealing with fundamental problems of the resolvent, Floquet theory, and total stability. Chapter 8 presents a solid foundation for the theory of functional differential equations. Many recent results on stability and periodic solutions of functional differential equations are given and unsolved problems are stated.
Key Features:
– Smooth transition from ordinary differential equations to integral and functional differential equations. – Unification of the theories, methods, and applications of ordinary and functional differential equations. – Large collection of examples of Liapunov functions. – Description of the history of stability theory leading up to unsolved problems. – Applications of the resolvent to stability and periodic problems. 1. Smooth transition from ordinary differential equations to integral and functional differential equations. 2. Unification of the theories, methods, and applications of ordinary and functional differential equations. 3. Large collection of examples of Liapunov functions. 4. Description of the history of stability theory leading up to unsolved problems. 5. Applications of the resolvent to stability and periodic problems.

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Table of contents :
Content:
Edited by
Page ii

Copyright page
Page iv

Preface
Pages ix-x

0 Introduction and Overview
Pages 1-4

1 The General Problems
Pages 5-21

2 Linear Equations
Pages 22-65

3 Existence Properties
Pages 66-96

4 History, Examples, and Motivation
Pages 97-123

5 Instability, Stability, and Perturbations
Pages 124-154

6 Stability and Boundedness
Pages 155-197

7 Perturbations
Pages 198-226

8 Functional Differential Equations
Pages 227-302

References
Pages 303-307

Author Index
Pages 309-310

Subject Index
Pages 311-313