Generalized solutions of functional differential equations

목차 (Table of Contents)

• CONTENTS
• Preface = ⅸ
• Chapter 1 Differential Equations with Piecewise Continuous Arguments = 1
• 1.1 Linear Retarded EPCA with Constant Coefficients = 4
• 1.2 Some Generalizations = 16
• 1.3 EPCA of Advanced, Mixed, and Neutral Types = 28
• 1.4 Asymptotic Behavior of Linear EPCA with Variable Coefficients = 51
• 1.5 Stability as a Function of Delay = 68
• 1.6 EPCA and Impulsive Equations = 72
• Chapter 2 Oscillatory and Periodic Solutions of Differential Equations with Piecewise Continuous Arguments = 81
• 2.1 Differential Inequalities with Piecewise Continuous Arguments = 82
• 2.2 Oscillatory Properties of First-Order Linear Functional Differential Equations = 91
• 2.3 Oscillatory and Periodic Solutions of Delay EPCA = 107
• 2.4 Differential Equations Alternately of Retarded and Advanced Type = 114
• 2.5 Oscillations in Systems of Differential Equations with Piecewise Continuous Arguments = 137
• 2.6 A Piecewise Constant Analogue of a Famous FDE = 157
• Chapter 3 Partial Differential Equations with Piecewise Continuous Delay = 163
• 3.1 Boundary-Value Problems for Partial Differential Equations with Piecewise Constant Delay = 164
• 3.2 Initial-Value Problems for Partial Differential Equations with Piecewise Constant Delay = 178
• 3.3 A Wave Equation with Discontinuous Time Delay = 190
• 3.4 Bounded Solutions of Retarded Nonlinear Hyperbolic Equations = 201
• Chapter 4 Reducible Functional Differential Equations = 213
• 4.1 Differential Equations with Involutions = 213
• 4.2 Linear Equations = 222
• 4.3 Bounded Solutions for Differential Equations with Reflection of the Argument = 235
• 4.4 Equations with Rotation of the Argument = 241
• 4.5 Boundary-Value Problems for Differential Equations with Reflection of the Argument = 249
• 4.6 Partial Differential Equations with Involutions = 265
• Chapter 5 Analytic and Distributional Solutions of Functional Differential Equations = 271
• 5.1 Holomorphic Solutions of Nonlinear Neutral Equations = 272
• 5.2 Holomorphic Solutions of Nonlinear Advanced Equations = 275
• 5.3 Analytic and Entire Solutions of Linear Systems = 279
• 5.4 Finite-Order Distributional Solutions = 292
• 5.5 Infinite-Order Distributional Solutions = 309
• 5.6 An Integral Equation in the Space of Tempered Distributions = 321
• Chapter 6 Coexistence of Analytic and Distributional Solutions for Linear Differential Equations = 325
• 6.1 Distributional, Rational, and Polynomial Solutions of Linear ODE = 326
• 6.2 Application to Orthogonal Polynomials = 330
• 6.3 Interesting Properties of Laguerre's Equation = 340
• 6.4 The Hypergeometric and Other Equations = 347
• 6.5 The Confluent Hypergeometric Equation = 359
• 6.6 Infinite-Order Distributional Solutions Revisited = 364
• Open Problems = 379
• Bibliography = 381
• Author Index = 399
• Subject Index = 403