Oscillation Theory for Difference and Functional Differential Equations - Hardcover

Agarwal, R.P.; Grace, Said R.; O'Regan, Donal

Hardcover

ISBN 10: 0792362896 ISBN 13: 9780792362890

Publisher: Springer, 2000

Synopsis

This monograph is devoted to a rapidly developing area of research of the qualitative theory of difference and functional differential equations. In fact, in the last 25 years Oscillation Theory of difference and functional differential equations has attracted many researchers. This has resulted in hundreds of research papers in every major mathematical journal, and several books. In the first chapter of this monograph, we address oscillation of solutions to difference equations of various types. Here we also offer several new fundamental concepts such as oscillation around a point, oscillation around a sequence, regular oscillation, periodic oscillation, point-wise oscillation of several orthogonal polynomials, global oscillation of sequences of real­ valued functions, oscillation in ordered sets, (!, R, ~)-oscillate, oscillation in linear spaces, oscillation in Archimedean spaces, and oscillation across a family. These concepts are explained through examples and supported by interesting results. In the second chapter we present recent results pertaining to the oscil­ lation of n-th order functional differential equations with deviating argu­ ments, and functional differential equations of neutral type. We mainly deal with integral criteria for oscillation. While several results of this chapter were originally formulated for more complicated and/or more general differ­ ential equations, we discuss here a simplified version to elucidate the main ideas of the oscillation theory of functional differential equations. Further, from a large number of theorems presented in this chapter we have selected the proofs of only those results which we thought would best illustrate the various strategies and ideas involved.

About this title

Synopsis

This text reviews material from more than 300 publications on the oscillation theory of difference and functional differential equations of various types. For difference equations, a large number of new concepts is explained and supported by theoretical developments. For differential equations, simplified versions of several new integral criteria for oscillations are presented. Proofs which illustrate the various strategies and ideas involved are given. This book should be a stimulus to the further development of the theory. It should be of interest to mathematicians and graduate students in the disciplines of theoretical and applied mathematics.

Edition details

• Publisher: Springer
• Publication date: 2000
• ISBN 10: 0792362896
• ISBN 13: 9780792362890
• Binding: Hardcover
• Language: English
• Number of pages: 346