陈宗煊编著的《复域差分与差分方程(英文版)(精)》介绍了，This book mainly contains the basic theory of complex differences, difference equa-tions and new results on this research field in recent years.Chapters 1-4 mainly introduce basic properties of complex differences and differ-ence polynomials. Chapters 5 to 9 are devoted to analytic properties of difference equa-tions. Chapter 10 deals with the value distribution of q-differences and q-differenceequations. Chapter 11 is concerned with the uniqueness problem.

Preface

List of Symbols

Chapter 1 Basic Properties of Complex Differences

 1.1 Preliminaries

 1.2 Difference Analogue of the Lemma on the Logarithmic Derivative -

 1.3 Estimations of N(r, f(z + η)

 1.4 Estimations of T(r, f(z + η)

 1.5 Difference Analogue of the Clunie Lemma

 1.6 Difference Analogue of the Mohon'ko Lemma

 1.7 Difference Analogue of the Second Main Theorem

 1.8 Characteristic Functions of △nf

Chapter 2 Relationships Between Meromorphic Functions and Differences

 2.1 Relationships of f(z) and △nf(z)

 2.2 Fixed Points of f(z), f(z + c) and △f(z)

Chapter 3 Differences of Meromorphic Functions with Small Growth

 3.1 Divided Differences of Entire Functions of order < 1

 3.2 Differences of Entire Functions of order≤ 1

 3.3 Differences of Meromorphic Functions

 3.4 Second Differences of Meromorphic Functions with Small Growth

Chapter 4 Properties of Difference Polynomials

 4.1 Difference Analogues of f(z)nf'(z)

 4.2 Difference Analogues of f'(z) - af(z)

 4.3 Difference Analogue of the Tumura-Clunie Type Theorems

Chapter 5 Linear First Order Difference Equations

 5.1 Equations Concerning Gamma Function

 5.2 General Linear First Order Difference Equations

 5.3 Differences of Solutions for Difference Equations, and Differences of r(z)

Chapter 6 Linear Higher Order Difference Equations

 6.1 Difference Equations with Rational Coefficients

 6.2 Difference Equations with Transcendental Coefficients

Chapter 7 Basic Properties of Nonlinear Difference Equations

 7.1 Basic Properties Concerning Order Number

 7.2 Properties of Meromorphic Solutions

Chapter 8 Difference Riccati Equations

 8.1 Pielou Logistic Equation

 8.2 Difference Riccati Equations

 8.3 A Family of Solutions for Difference Riccati Equations

Chapter 9 Difference Painleve Equations

 9.1 Classified of Second Difference Equations

 9.2 Difference PainleveⅡ Equations

 9.3 Difference Painleve Ⅰ Equations

 9.4 Difference Painleve Ⅲ Equations

Chapter 10 Complex q-Differences and q-Difference Equations

 10.1 Properties of q-Differences

 10.2 Linear q-Difference Equations

 10.3 Non-Linear q-Difference Equations

 10.4 q-Difference Riceati equations

Chapter 11 Unicity of Meromorphic Functions Concerning Their Differences and Shifts

 11.1 Meromorphic Functions f(z) that Share Values with f(z + c)

 11.2 Meromorphic Functions f(z) that Share Values with △f(z)

 11.3 Meromorphic Functions f(z) that Share Values with △f(z) and△2/(z)

 11.4 Meromorphic Functions f(z) that Share Values with △nf(z)

Bibliography

Index