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.
Author(s): Said R. Grace, Donal O'Regan, Ravi P. Agarwal
Edition: 1
Publisher: Kluwer Academic Publishers
Year: 2000
Language: English
Pages: 346
City: Dordrecht; Boston
Tags: Математика;Дифференциальные уравнения;
Front cover......Page 1
Title page......Page 3
Date-line......Page 4
Contents......Page 5
Preface......Page 7
1.1. Introduction......Page 9
1.2. Oscillation of Scalar Difference Equations......Page 10
1.3. Oscillation of Orthogonal Polynomials......Page 16
1.4. Oscillation of Functions Recurrence Equations......Page 22
1.5. Oscillation in Ordered Sets......Page 27
1.6. Oscillation in Linear Spaces......Page 30
1.7. Oscillation in Archimedean Spaces......Page 32
1.8. Oscillation of Partial Recurrence Equations......Page 35
1.9. Oscillation of System of Equations......Page 40
1.10. Oscillation Between Sets......Page 44
1.11. Oscillation of Continuous-Discrete Recurrence Equations......Page 47
1.12. Second Order Quasilinear Difference Equations......Page 50
1.13. Oscillation of Even Order Difference Equations......Page 64
1.14. Oscillation of Odd Order Difference Equations......Page 73
1.15. Oscillation of Neutral Difference Equations......Page 81
1.16. Oscillation of Mixed Difference Equations......Page 87
1.17. Difference Equations Involving Quasi-differences......Page 102
1.18. Difference Equations with Distributed Deviating Arguments......Page 125
1.19. Oscillation of Systems of Higher Order Difference Equations......Page 151
1.20. Partial Difference Equations with Continuous Variables......Page 157
2.1. Introduction......Page 174
2.2. Definitions, Notations and Preliminaries......Page 175
2.3. Ordinary Differential Equations......Page 181
2.4. Functional Differential Equations......Page 188
2.5. Comparison of Equations of the Same Form......Page 207
2.6. Comparison of Equations with Others of Lower Order......Page 213
2.7. Further Comparison Results......Page 216
2.8. Equations with Middle Term of Order $(n-1)$......Page 233
2.9. Forced Differential Equations......Page 243
2.10. Forced Equations with Middle Term of Order $(n-1)$......Page 250
2.11. Superlinear Forced Equations......Page 252
2.12. Sublinear Forced Equations......Page 255
2.13. Perturbed Functional Equations......Page 257
2.14. Comparison of Neutral Equations with Nonneutral Equations......Page 260
2.15. Comparison of Neutral Equations with Equations of the Same Form......Page 269
2.16. Neutral Differential Equations of Mixed Type......Page 273
2.17. Functional Differential Equations Involving Quasi-derivatives......Page 283
2.18. Neutral and Damped Functional Differential Equations Involving Quasi-derivatives......Page 294
2.19. Forced Functional Differential Equations Involving Quasi-derivatives......Page 299
2.20. Systems of Higher Order Functional Differential Equations......Page 317
References......Page 326
Subject Index......Page 344
Back cover......Page 346
