Oscillation Theory for Difference and Functional Differential Equations

by Agarwal, Ravi P.; Grace, Said R.; O'Regan, D.

• ISBN13: 9780792362890
• ISBN10: 0792362896
• Format: Hardcover
• Copyright: 2000-05-01
• Publisher: Kluwer Academic Pub

Summary

This book reviews material from more than three hundred publications on the oscillation theory of difference and functional differential equations of various types. For difference equations, a large number of new concepts are explained and supported by interesting 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. Audience: This work will be of interest to mathematicians and graduate students in the disciplines of theoretical and applied mathematics.

Table of Contents

Preface	vii
Oscillation of Difference Equations
Introduction	1	(1)
Oscillation of Scalar Difference Equations	2	(6)
Oscillation of Orthogonal Polynomials	8	(6)
Oscillation of Functions Recurrence Equations	14	(5)
Oscillation in Ordered Sets	19	(3)
Oscillation in Linear Spaces	22	(2)
Oscillation in Archimedean Spaces	24	(3)
Oscillation of Partial Recurrence Equations	27	(5)
Oscillation of System of Equations	32	(4)
Oscillation Between Sets	36	(3)
Oscillation of Continuous-Discrete Recurrence Equations	39	(3)
Second Order Quasilinear Difference Equations	42	(14)
Oscillation of Even Order Difference Equations	56	(9)
Oscillation of Odd Order Difference Equations	65	(8)
Oscillation of Neutral Difference Equations	73	(6)
Oscillation of Mixed Difference Equations	79	(15)
Difference Equations Involving Quasi-differences	94	(23)
Difference Equations with Distributed Deviating Arguments	117	(26)
Oscillation of Systems of Higher Order Difference Equations	143	(6)
Partial Difference Equations with Continuous Variables	149	(17)
Oscillation of Functional Differential Equations
Introduction	166	(1)
Definitions, Notations and Preliminaries	167	(6)
Ordinary Differential Equations	173	(7)
Functional Differential Equations	180	(19)
Comparison of Equations of the Same Form	199	(6)
Comparison of Equations with Others of Lower Order	205	(3)
Further Comparison Results	208	(17)
Equations with Middle Term of Order (n - 1)	225	(10)
Forced Differential Equations	235	(7)
Forced Equations with Middle Term of Order (n - 1)	242	(2)
Superlinear Forced Equations	244	(3)
Superlinear Forced Equations	247	(2)
Perturbed Functional Equations	249	(3)
Comparison of Neutral Equations with Nonneutral Equations	252	(9)
Comparison of Neutral Equations with Equations of the Same Form	261	(4)
Neutral Differential Equations of Mixed Type	265	(10)
Functional Differential Equations Involving Quasi-derivatives	275	(11)
Neutral and Damped Functional Differential Equations Involving Quasi-derivatives	286	(5)
Forced Functional Differential Equations Involving Quasi-derivatives	291	(18)
Systems of Higher Order Functional Differential Equations	309	(9)
References	318	(18)
Subject Index	336