Advanced Topics in Difference Equations [1 ed.] 0792345215, 9780792345213

Table of contents :
Front Matter....Pages i-ix
Periodic Solutions of First Order Linear Equations....Pages 1-11
Periodic Solutions of Generalized Difference Systems....Pages 11-26
Periodic Boundary Value Problems: First Order Systems....Pages 26-33
Periodic Boundary Value Problems: Second Order Systems....Pages 33-40
Periodic Solutions of Higher Order Partial Difference Equations....Pages 41-61
Nonlinear Variation of Parameter Methods: One Independent Variable....Pages 61-74
Nonlinear Variation of Parameter Methods: Several Independent Variables....Pages 74-84
Convergence to Equilibria....Pages 84-96
Asymptotic Behavior of Generalized Difference Systems....Pages 96-105
Stability of Generalized Difference Systems....Pages 105-112
Oscillation via Lyapunov’s Second Method....Pages 112-121
Oscillation via Difference Inequalities....Pages 121-134
Oscillation via Summation Averages....Pages 134-149
Oscillation for Nonlinear Difference Equations....Pages 149-166
Oscillation for Quasilinear Difference Equations....Pages 167-172
Oscillations Generated by Deviating Arguments....Pages 172-189
Positive Monotone Solutions for Nonlinear Difference Equations....Pages 189-197
Oscillation for n th Order Nonlinear Difference Equations....Pages 197-209
Comparison Theorems....Pages 209-219
Oscillation for Second Order Neutral Delay Difference Equations....Pages 219-227
Oscillation for Second Order Neutral Delay Difference Equations (Contd.)....Pages 227-233
Oscillation for Higher Order Neutral Delay Difference Equations....Pages 233-241
Oscillation for Partial Difference Equations I....Pages 241-271
Oscillation for Partial Difference Equations II....Pages 271-276
Oscillation for Partial Difference Equations III....Pages 277-296
Oscillation for Partial Difference Equations IV....Pages 296-310
A Three-Point Boundary Value Problem....Pages 311-318
A Singular Boundary Value Problem....Pages 318-329
Eigenvalues of Boundary Value Problems....Pages 329-350
Two Solutions of a Boundary Value Problem....Pages 350-361
( n , p ) Boundary Value Problems....Pages 361-384
Boundary Value Problems Arising in Transport Phenomena....Pages 384-398
Solutions of m -Point Boundary Value Problems....Pages 398-413
Two-Point Boundary Value Problems for Generalized Difference Systems....Pages 414-425
Multi-Point Boundary Value Problems for Generalized Difference Systems....Pages 425-448
Resonant Boundary Value Problems for Generalized Difference Systems....Pages 449-464
Boundary Value Problems in Abstract Spaces....Pages 464-470
Linear Square Optimal Control Problem....Pages 471-478
Symmetries of Difference Systems on Manifolds....Pages 478-483
Discrete Polar Coordinates....Pages 483-491
Back Matter....Pages 492-510