Discrete Oscillation Theory (Contemporary Mathematics and Its Applications Book Series) by Ravi P. Agarwal (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “…By my opinion, every researcher in the qualitative theory of difference equations should have this book in his/her bookshelf.” — Zentralblatt MATH Database, (2006; Zbl 1084.39001)

“…It is written by mathematicians who achieved remarkable results in this area.” — Zentralblatt MATH Database, (2006; Zbl 1084.39001)

“…The book can be used as textbook at graduate level and as reference book; bibliography contains almost 300 items.” — Zentralblatt MATH Database, (2006; Zbl 1084.39001)

“It is indeed a useful addition to the literature to have such a comprehensive survey of the area” — MathSciNet – MR2179948(Review)-American Mathematical Society

“It will serve as a valuable reference in the area for many years to come” — MathSciNet – MR2179948(Review)-American Mathematical Society

“This huge monograph surveys recent development in the rapidly growing area of discrete oscillation theory. It summarizes the results of almost three hundred research papers including background material, full proofs and hints with respect to the original literature. The easy level makes it suitable not only as a valuable resource for researchers, but also for undergraduate students. Personally I missed results on the connection between discrete oscillation theory and respectral theory. Nevertheless I find it a useful contribution to the literature in the field by four of the leading experts” –Book Review published in Monatshefte für Mathematik; Vol. 150, No.1/2007; by G. Teschl, Wien

“This is truly a compendium of many different results” –MathSciNet – MR2179948(Review)-American Mathematical Society About the Author 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.

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