Discrete Oscillation Theory

by Agarwal, Ravi P.; Bohner, Martin; Grace, Said R.; O'Regan, Donal

• ISBN13: 9789775945198
• ISBN10: 9775945194
• Format: Hardcover
• Copyright: 2005-08-31
• Publisher: Hindawi Pub Corp

Summary

This book is devoted to a rapidly developing branch of the qualitative theory of difference equations with or without delays. It presents the theory of oscillation of difference equations, exhibiting classical as well as very recent results in that area. While there are several books on difference equations and also on oscillation theory for ordinary differential equations, there is until now no book devoted solely to oscillation theory for difference equations. This book is filling the gap, and it can easily be used as an encyclopedia and reference tool for discrete oscillation theory.In nine chapters, the book covers a wide range of subjects, including oscillation theory for second-order linear difference equations, systems of difference equations, half-linear difference equations, nonlinear difference equations, neutral difference equations, delay difference equations, and differential equations with piecewise constant arguments. This book summarizes almost 300 recent research papers and hence covers all aspects of discrete oscillation theory that have been discussed in recent journal articles. The presented theory is illustrated with 121 examples throughout the book. Each chapter concludes with a section that is devoted to notes and bibliographical and historical remarks.The book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists, and physicists. Besides serving as a reference tool for researchers in difference equations, this book can also be easily used as a textbook for undergraduate or graduate classes. It is written at a level easy to understand for college students who have had courses in calculus.

Author Biography

Ravi P. Agarwal is a professor of mathematics at Florida Institute of Technology, Melbourne, USA. He has been the Editor or Associate Editor of 35 journals or book series and is the author or coauthor of over 600 journal articles and more than 16 books. Dr. Agarwal received the Ph.D. degree (1973) in mathematics from the Indian Institute of Technology, Mardas, India. Martin Bohner works at the University of Missouri-Rolla, USA. The editor and the author of wide range of professional publications in the areas of differential equations, difference equations, and dynamic equations on time scales, he is an Alexander von Humboldt Fellow and Vice President of the International Society of Difference Equations. Dr. Bohner received his Ph.D. degree (1995) in natural science from the University of Ulm, Germany. Said R. Grace is a Professor in the Department of Engineering Mathematics at Cairo University, Egypt. He is the author of more than 200 journal articles and 4 books. Dr. Grace received the Ph.D. degree (1981) in mathematics from the University of Saskatchewan, Canada. Donal O'regan works at the National University of Ireland, Galway, Irelad. His research interest is nonlinear analysis; in particular, fixed point theory, operator, differential, integral equations, and inclusions and oscillation theory. He received the Ph.D. degree (1985) in mathematics from Oregon State University, USA.