The Comparation Of Maximum Modulus Of Analytic Functions And Growth Of Solutions Of Complex Linear Differential Equations With Entire Coefficient Of Finite Logarithmic Order

In this paper we use the growth of entire function and analytic function to compare the growth of their maximum modulus M(r,f)with those of their derivative functions(i.e.M'(r,f)),we also investigate the growth of solutions of high order linear differential equations with entire coefficients of finite logarithmic order.The thesis is divided into three chapters.In chapter 1,we introduce some basic definitions and notations about entire function,analytic function and meromorphic function.In chapter 2,we make use of the order,type of entire function or analytic function to compare the growth of M(r,f)with M'(r,f),and we also work out the existence conditions of proximate type for entire function and analytic function.In chapter 3,we study the growth and zeros of solutions of high order linear differential equation with entire coefficients of finite logarithmic order,the results we obtain improve some previous results.