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.
- 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
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1. The General Problems
2. Linear Equations
3. Existence Properties
4. History, Examples and Motivation
5. Instability, Stability and Perturbations
6. Stability and Boundedness
7. The Resolvent
8. Functional Differential Equations