Advanced Topics in Difference Equations

By: R.P. Agarwal, Patricia J.Y. Wong

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Hardcover | 30 April 1997

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524 Pages

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. The theory of difference equations, the methods used in their solutions and their wide applications have advanced beyond their adolescent stage to occupy a central position in Applicable Analysis. In fact, in the last five years, the proliferation of the subject is witnessed by hundreds of research articles and several monographs, two International Conferences and numerous Special Sessions, and a new Journal as well as several special issues of existing journals, all devoted to the theme of Difference Equations. Now even those experts who believe in the universality of differential equations are discovering the sometimes striking divergence between the continuous and the discrete. There is no doubt that the theory of difference equations will continue to play an important role in mathematics as a whole. In 1992, the first author published a monograph on the subject entitled Difference Equations and Inequalities. This book was an in-depth survey of the field up to the year of publication. Since then, the subject has grown to such an extent that it is now quite impossible for a similar survey, even to cover just the results obtained in the last four years, to be written. In the present monograph, we have collected some of the results which we have obtained in the last few years, as well as some yet unpublished ones.

Industry Reviews

`I think this remarkable monograph should be on the bookshelf of veryone having connection with mathematical analysis and its applications, concentrating on difference equations, numerical analysis, ordinary and partial differential equations.'
Acta Sci. Math., 64 (1998)

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Preface
Periodic Solutions of First Order Linear Equations	p. 1
Periodic Solutions of Generalized Difference Systems	p. 11
Periodic Boundary Value Problems: First Order Systems	p. 26
Periodic Boundary Value Problems: Second Order Systems	p. 33
Periodic Solutions of Higher Order Partial Difference Equations	p. 41
Nonlinear Variation of Parameter Methods: One Independent Variable	p. 61
Nonlinear Variation of Parameter Methods: Several Independent Variables	p. 74
Convergence to Equilibria	p. 84
Asymptotic Behavior of Generalized Difference Systems	p. 96
Stability of Generalized Difference Systems	p. 105
Oscillation via Lyapunov's Second Method	p. 112
Oscillation via Difference Inequalities	p. 121
Oscillation via Summation Averages	p. 134
Oscillation for Nonlinear Difference Equations	p. 149
Oscillation for Quasilinear Difference Equations	p. 167
Oscillations Generated by Deviating Arguments	p. 172
Positive Monotone Solutions for Nonlinear Difference Equations	p. 189
Oscillation for nth Order Nonlinear Difference Equations	p. 197
Comparison Theorems	p. 209
Oscillation for Second Order Neutral Delay Difference Equations	p. 219
Oscillation for Second Order Neutral Delay Difference Equations (Contd.)	p. 227
Oscillation for Higher Order Neutral Delay Difference Equations	p. 233
Oscillation for Partial Difference Equations I	p. 241
Oscillation for Partial Difference Equations II	p. 271
Oscillation for Partial Difference Equations III	p. 277
Oscillation for Partial Difference Equations IV	p. 296
A Three-Point Boundary Value Problem	p. 311
A Singular Boundary Value Problem	p. 318
Eigenvalues of Boundary Value Problems	p. 329
Two Solutions of a Boundary Value Problem	p. 350
(n,p) Boundary Value Problems	p. 361
Boundary Value Problems Arising in Transport Phenomena	p. 384
Solutions of m-Point Boundary Value Problems	p. 398
Two-Point Boundary Value Problems for Generalized Difference Systems	p. 414
Multi-Point Boundary Value Problems for General Difference Systems	p. 425
Resonant Boundary Value Problems for Generalized Difference Systems	p. 449
Boundary Value Problems in Abstract Spaces	p. 464
Linear Square Optimal Control Problem	p. 471
Symmetries of Difference Systems on Manifolds	p. 478
Discrete Polar Coordinates	p. 483
References	p. 492
Table of Contents provided by Blackwell. All Rights Reserved.

Advanced Topics in Difference Equations

At a Glance

Hardcover

Industry Reviews

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Defective items

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