The Growth Of Solutions Of Some Classes Of Complex Linear Differential Equations

In this thesis,we investigate the growth of complex linear differential equations by using Nevanlinna theory.This thesis is made up of three chapters.The relevant knowledge of Nevanlinna theory is recalled and the progress of solu-tions of complex differential equations is introduced in the chapter 1.The growth of solution of second order linear differential equation f?+ A(z)f? + B(z)f = 0 is discussed by using a new method in the chapter 2,where A(z)and B(z)are nontivial solutions of differential equations w? + Q1(z)w = 0 and w? + Q2(z)w=0 respectively,where Qi(z)and Q2(z)are polynomials,The relationship between the solutions of the equation and the cofficient is obtained.We define the logarithmic ? order and logarithmic ? form of meromorphic function on complex plane and We study the growth of solutions of higher order linear differential equation f(k)(z)+ A(k-1)(z)f(k-1)(z)+…+ A0(z)f(z)= 0 in the chapter 3,where Ai(z)are entire functions with finite logarithmic ? order,i = 0,1,2…,k-1.