Theory of Differential Equations with Unbounded Delay

Softcover Nachdruck of the original 1. Auflage 1994
ISBN: 978-1-4613-6116-9
Verlag: Springer US

Buch, Englisch, Band 298, 386 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 604 g

Reihe: Mathematics and Its Applications

Because the theory of equations with delay terms occurs in a variety of contexts, it is important to provide a framework, whenever possible, to handle as many cases as possible simultaneously so as to bring out a better insight and understanding of the subtle differences of the various equations with delays. Furthermore, such a unified theory would avoid duplication and expose open questions that are significant for future research.
It is in this spirit that the authors view the importance of their monograph, which presents a systematic and unified theory of recent developments of equations with unbounded delay, describes the current state of the theory showing the essential unity achieved, and provides a general structure applicable to a variety of problems.
It is the first book that:
(i) presents a unified framework to investigate the basic existence theory for a variety of equations with delay;
(ii) treats the classification of equations with memory precisely so as to bring out the subtle differences between them;
(iii) develops a systematic study of stability theory in terms of two different measures which includes several known concepts; and
(iv) exhibits the advantages of employing Lyapunov functions on product spaces as well as the method of perturbing Lyapunov functions.
This book will be of value to researchers and advanced graduate students in mathematics, electrical engineering and biomathematics.

Zielgruppe

Research

Autoren/Hrsg.

Lakshmikantham, V.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Preface. 1. Preliminaries. 2. Existence Theory for p-Type NFDE. 3. Existence Theory of NFDE with Infinite Delay. 4. Stability and Boundedness for RFDE with Bounded Delay. 5. Stability Criteria for p-Type NFDE. 6. Stability and Boundedness for Equations with Infinite Delay. 7. Asymptotic Behavior. 8. Oscillation Theory. 9. Periodic Solutions. References. Index.