Oscillation Theory for Difference and Functional Differential Equations,9780792362890

Oscillation Theory for Difference and Functional Differential Equations

by ; ;
ISBN13: 9780792362890
ISBN10: 0792362896
Format: Hardcover
Pub. Date: 2000-05-01
Publisher(s): Kluwer Academic Pub
List Price: $151.25

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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

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