Generalized solutions of functional differential equations

Cover......Page 1
S Title......Page 2
GENERALIZED SOLUTIONS OF FUNCTI ONALDIFFERENTIAL EQUATIONS......Page 4
ISBN 981-02-1207-0......Page 5
Contents......Page 6
Preface......Page 10
CHAPTER 1  Differential Equations with Piecewise Continuous Arguments......Page 15
1. Linear Retarded EPCA with Constant Coefficients......Page 18
2. Some Generalizations......Page 30
3. EPCA of Advanced, Mixed, and Neutral Types......Page 42
4. Asymptotic Behavior of Linear EPCA with Variable Coefficients......Page 65
5. Stability as a Function of Delay......Page 82
6. EPCA and Impulsive Equations......Page 86
CHAPTER 2  Oscillatory and Periodic Solutions of Differential Equations with Piecewise Continuous Arguments......Page 95
1. Differential Inequalities with Piecewise  continuous Arguments......Page 96
2. Oscillatory Properties of First-Order Linear Functional Differential Equations......Page 105
3. Oscillatory and Periodic Solutions of Delay EPCA......Page 121
4. Differential Equations Alternately of Retarded and Advanced Type......Page 128
5. Oscillations in Systems of Differential Equations with Piecewise Continuous Arguments......Page 151
6. A Piecewise Constant Analogue of a Famous FDE......Page 171
CHAPTER 3  Partial Differential Equations with Piecewise Continuous Delay......Page 177
1. Boundary-Value Problems for Partial Differential Equations with Piecewise Constant Delay......Page 178
2. Initial-Value Problems for Partial Differential Equations with Piecewise Constant Delay......Page 192
3. A Wave Equation with Discontinuous Time Delay......Page 204
4. Bounded Solutions of Retarded Nonlinear Hyperbolic Equations......Page 215
1. Differential Equations with Involutions......Page 227
2. Linear Equations......Page 236
3. Bounded Solutions for Differential Equations with Reflection of the Argument......Page 249
4. Equations with Rotation of the Argument......Page 255
5.1. Preliminary Results. F......Page 263
5.2. Main Results. ......Page 265
6. Partial Differential Equations with Involutions......Page 279
CHAPTER 5  Analytic and Distributional Solutions of Functional Differential Equations......Page 285
1. Holomorphic Solutions of Nonlinear Neutral Equations......Page 286
2. Holomorphic Solutions of Nonlinear Advanced Equations......Page 289
3. Analytic and Entire Solutions of Linear Systems......Page 293
4. Finite-Order Distributional Solutions......Page 306
5. Infinite-Order Distributional Solutions......Page 323
6. An Integral Equation in the Space of Tempered Distributions......Page 335
CHAPTER 6  Coexistence of Analytic and Distributional Solutions for Linear Differential Equations......Page 339
1. Distributional, Rational, and Polynomial Solutions of Linear ODE......Page 340
2. Application to Orthogonal Polynomials......Page 344
3. Interesting Properties of Laguerre\'s Equation......Page 354
4. The Hypergeometric and Other Equations......Page 361
5. The Confluent Hypergeometric Equation......Page 373
6. Infinite-Order Distributional Solutions Revisited......Page 378
Open Problems......Page 393
Bibliography......Page 395
Author Index......Page 413
Subject Index......Page 417
Back Cover......Page 424