The Complex Oscillation Properties Of Solutions Of Several Types Of Complex Differential Equations

This paper is divided into five chapters.The main content of this paper is to studies the oscillation of the solutions of the differential equations in the complex domain.The first chapter mainly introduces the relevant preparation theory knowledge.In the second chapter,the properties of the characteristic function in the sub pure function are studied.Based on the knowledge of the value distribution theory,a more general form of the characteristic function inequality is obtained.In the third chapter,the growth of solutions of a class of two order complex differential equations is studied ,Among them,is the entire function,P_j (z)is a n degree polynomial,coefficient of growth leve ?(A_j)?n.This paper,according to property of corresponding to the higher order differential equation,the nature of the promotion to second order complex differential equation,using the value distribution theory of the theorem and method,the feasibility of applying the lemma and its proof commonly used in anyway method,the accurate estimation of level.In the fourth chapter,this paper mainly studies the analytic functions in the unit circle of higher order homogeneous linear differential equation and non-homogeneous linear differential equation solution of the relationship between and the first-order derivative and second-order derivative and small functions,and obtain the precise estimates between them.The fifth chapter summarizes the main research content of this paper and its prospects.