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This book presents developments and new results on complex differential-difference equations, an area with important and interesting applications, which also gathers increasing attention. Key problems, methods, and results related to complex differential-difference equations are collected to offer an up-to-date overview of the field.

Complex Delay-Differential Equations

Preface

Content

Chapter 1: Introduction to Nevanlinna theory and its difference version

1.1: Nevanlinna theory

1.2 Difference analogue of Nevanlinna theory

Chapter 2: Value distribution of complex differential-difference polynomials

2.1 Differential-difference versions of standard classical results

2.2 Uniqueness theory for complex D-D polynomials

Chapter 3: Local theory of complex differential-difference equations

3.1 Power series solutions

3.2 Fixed points

Chapter 4; Linear complex differential-difference equations

4.1 Operator theory

4.2 Infinite order differential equations

4.3 First order D-D equations

4.4 Higher order D-D equations

Chapter 5: Nonlinear complex differential-difference equations

5.1 Fermat type D-D equations

5.2 Riccati type D-D equations

5.3 Malmquist type D-D equations

5.4 Other non-linear D-D equations

Chapter 6: Complex q-difference differential equations

Chapter 7: Systems of complex differential-difference equations

Chapter 8: Applications

Bibliography