| ABSTRACT | 第4页 |
| 摘要 | 第5-8页 |
| CHAPTER | 第8页 |
| Ⅰ. Introduction | 第8-14页 |
| 1.1 The history and methods of complex linear differential equations | 第8-11页 |
| 1.2 The outline of properties of solutions of complex linear differential equations | 第11-14页 |
| Ⅱ. The Zero Distribution of Solutions of Second Order Linear Differential Equations in Angular Domain | 第14-41页 |
| 2.1 Basic definitions and preliminaries | 第14-17页 |
| 2.2 Relationship between σ(Ω(α,β),g) and ρ(Ω(α,β),9) | 第17-21页 |
| 2.3 The properties of characteristic function in an angular domain | 第21-26页 |
| 2.4 The zeros distribution of solutions of second order linear differential equations | 第26-41页 |
| Ⅲ. The Zero Distribution of Solutions of Higher Order Linear Differential Equations in Angular Domain | 第41-51页 |
| 3.1 The zeros distribution of solutions of higher order linear differential equations | 第41-48页 |
| 3.2 The relation between a cluster ray of zeros and Borel direction | 第48-51页 |
| Ⅳ. Representations of Subnormal Solutions of Linear Differential Equations with Periodic Coefficients | 第51-89页 |
| 4.1 Subnormal solutions of f″+P_1(e~z)f′+P_2(e~z)f=0 | 第51-56页 |
| 4.2 Subnormal solutions of f″+P_1(e~z)f′+P_2(e~z)f′=R_1(e~z)+R_2(e~(-z)) | 第56-57页 |
| 4.3 Subnormal solutions of f″+[P_1(e~z)+Q_1(e~(-z))]f′+[P_2(e~z)+Q_2(e~(-z))]f=0 | 第57-67页 |
| 4.4 Subnormal solutions of f″+[P_1(e~z)+Q_1(e~(-z))]f′+[P_2(e~z)+Q_2(e~(-z))]f=R_1(e~z)+R_2(e~(-z)) | 第67-85页 |
| 4.5 Subnormal solutions of f~((n))+[P_(n-1)(e~z)+Q_(n-1)(e~(-z))]f~((n-1))+…+[P_1(e~z)+Q_1(e~(-z))]f′+[P_0(e~z))+Q_0(e~(-z))]f=R_1(e~z)+R_2(e~(-z)) | 第85-87页 |
| 4.6 Examples Satisfying the Theorems | 第87-89页 |
| Ⅴ. Perturbation Results of Second Order Linear Differential Equations with Periodic Coefficients | 第89-105页 |
| 5.1 Properties of e-type order and e-type exponent of convergence of zeros | 第89-92页 |
| 5.2 Nevanlinna characteristic functions in |z|>R_0 | 第92-93页 |
| 5.3 The properties of f″+A(z)f=0 | 第93-94页 |
| 5.4 The perturbation results of f″+{Ⅱ(z)+A(z)}f=0 | 第94-95页 |
| 5.5 The perturbation results of f″+Ⅱ(z)A(z)f=0 | 第95-103页 |
| 5.6 The perturbation results of f″+{Ⅱ(z)A(z)+exp(P(e~z))}f=0 | 第103-105页 |
| BIBLIOGRAPHY | 第105-110页 |
| ACKNOWLEDGEMENTS | 第110-111页 |
