Stability of differential equations with aftereffect.

*(English)*Zbl 1049.34090
Stability and Control: Theory, Methods and Applications 20. London: Taylor and Francis (ISBN 0-415-26957-1). xviii, 222 p. (2003).

Due to the complexities involved in various real world processes, their mathematical descriptions lead to complicated differential equations. The study of such systems offers more challenges and helps us to understand these processes precisely.

The present monograph is an outcome of serious research spread over a few decades. The authors do a fairly good job of picking out the material relevant to this topic and an excellent survey of the earlier literature is presented.

There are essentially five chapters in this monograph. The following is the description of the contents of these chapters.

Chapter 1 discusses all the necessary information on functional-differential equations. Chapter 2 deals with examples of \(D\)-space constructions and \(D\)-stability tests. Chapters 3 and 4 consider the problem of solvability of the Cauchy problem under more special spaces. The final chapter is devoted to the stability of nonlinear systems.

The presentation is very lucid and readers can easily understand the material presented in this monograph. It is the reviewer’s opinion that this monograph is a good resource for specialists as well as beginners in this fascinating field.

The present monograph is an outcome of serious research spread over a few decades. The authors do a fairly good job of picking out the material relevant to this topic and an excellent survey of the earlier literature is presented.

There are essentially five chapters in this monograph. The following is the description of the contents of these chapters.

Chapter 1 discusses all the necessary information on functional-differential equations. Chapter 2 deals with examples of \(D\)-space constructions and \(D\)-stability tests. Chapters 3 and 4 consider the problem of solvability of the Cauchy problem under more special spaces. The final chapter is devoted to the stability of nonlinear systems.

The presentation is very lucid and readers can easily understand the material presented in this monograph. It is the reviewer’s opinion that this monograph is a good resource for specialists as well as beginners in this fascinating field.

Reviewer: V. Sree Hari Rao (MR 2004f:34110)