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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.
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