On Meromorphic Solutions Of A Class Of Algebraic Differential Equations

In recent 30 years, studying meromorphic solutions of algebraic differential equations is an important issue in complex analysis. In this thesis, we study the estimates for the number of linearly independent meromorphic solutions and for distinct meromorphic solutions of a class of algebraic differential equations, and obtain two results. The two results generalize Gundersen's [22] relative results.This thesis consists of six chapters. The first chapter introduces the thesis' studying work, studying purpose, background and so on. The second chapter briefly outlines the background and basic knowledge of algebraic differential equations,and introduces scholars estimated the maximum number of distinct meromorphic solutions and linearly independent meromorphic solutions of the first order algebraic differential equations with polynomial coefficients, including: Gundersen,Laine, He Yuzan, Yuan Wenjun and so on. At the same time, it outlines many scholars generalized the first order differential equations with polynomial coefficients to the first order differential equations with rational coefficients, such as Gao Shian!Zhang Xiaokuan and Tan Yuewu. At last, it also introduces the results of a class of algebraic differential equations with particular coefficients. The third chapter introduces some fundamental theorem of Nevanlinna value distribution theory and some theorems and lemmas which will proof Theorem 4.1 and Theorem 5.1. In the fourth and the fifth chapter we introduce our two results:Theorem 4.1 and Theorem 5.1 and proof them. In the last chapter, we give some open questions.