Complex Delay-Differential Equations

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.

Auteur
Kai Liu, Nanchang University, China; Ilpo Laine, University of Eastern Finland, Finland; Lianzhong Yang, Shandong University, China.

Résumé

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist.

The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level.

The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.
While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community.

Please submit any book proposals to Niels Jacob.

Contenu

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