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Advanced Topics in Difference Equations : Mathematics and Its Applications - Ravi P. Agarwal

Advanced Topics in Difference Equations

Mathematics and Its Applications

Hardcover Published: 30th April 1997
ISBN: 9780792345213
Number Of Pages: 510

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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monograph, we have collected some of the results which we have obtained in the last few years, as well as some yet unpublished ones.

`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)

Preface
Periodic Solutions of First Order Linear Equationsp. 1
Periodic Solutions of Generalized Difference Systemsp. 11
Periodic Boundary Value Problems: First Order Systemsp. 26
Periodic Boundary Value Problems: Second Order Systemsp. 33
Periodic Solutions of Higher Order Partial Difference Equationsp. 41
Nonlinear Variation of Parameter Methods: One Independent Variablep. 61
Nonlinear Variation of Parameter Methods: Several Independent Variablesp. 74
Convergence to Equilibriap. 84
Asymptotic Behavior of Generalized Difference Systemsp. 96
Stability of Generalized Difference Systemsp. 105
Oscillation via Lyapunov's Second Methodp. 112
Oscillation via Difference Inequalitiesp. 121
Oscillation via Summation Averagesp. 134
Oscillation for Nonlinear Difference Equationsp. 149
Oscillation for Quasilinear Difference Equationsp. 167
Oscillations Generated by Deviating Argumentsp. 172
Positive Monotone Solutions for Nonlinear Difference Equationsp. 189
Oscillation for nth Order Nonlinear Difference Equationsp. 197
Comparison Theoremsp. 209
Oscillation for Second Order Neutral Delay Difference Equationsp. 219
Oscillation for Second Order Neutral Delay Difference Equations (Contd.)p. 227
Oscillation for Higher Order Neutral Delay Difference Equationsp. 233
Oscillation for Partial Difference Equations Ip. 241
Oscillation for Partial Difference Equations IIp. 271
Oscillation for Partial Difference Equations IIIp. 277
Oscillation for Partial Difference Equations IVp. 296
A Three-Point Boundary Value Problemp. 311
A Singular Boundary Value Problemp. 318
Eigenvalues of Boundary Value Problemsp. 329
Two Solutions of a Boundary Value Problemp. 350
(n,p) Boundary Value Problemsp. 361
Boundary Value Problems Arising in Transport Phenomenap. 384
Solutions of m-Point Boundary Value Problemsp. 398
Two-Point Boundary Value Problems for Generalized Difference Systemsp. 414
Multi-Point Boundary Value Problems for General Difference Systemsp. 425
Resonant Boundary Value Problems for Generalized Difference Systemsp. 449
Boundary Value Problems in Abstract Spacesp. 464
Linear Square Optimal Control Problemp. 471
Symmetries of Difference Systems on Manifoldsp. 478
Discrete Polar Coordinatesp. 483
Referencesp. 492
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792345213
ISBN-10: 0792345215
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 510
Published: 30th April 1997
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 2.87
Weight (kg): 0.9