The Properties Of Analytic Function With Relative Order In The Unit Disc And Their Applications To Second-order Complex Linear Differential Equations

In this thesis,we use some basic knowledge of Nevanlinna value distribution theory to study the properties of the relative order of function f(z)which is analytic in the unit disc.And we consider the growth of solutions of second-order complex linear differential equations.The paper is divided into three chapters.In chapter 1,we introduce some basic definitions and common notations of the Nevanlinna value distribution theory.In chapter 2,we study the relationship between the relative order of functions analytic in the unit disc pg(f)and the relative order defined by its maximum modulus which we called ρgM(f).Meanwhile we consider the magnitude relationship between the relative order of function f(z)and the relative order of f’(z),we extend some previous results.In chapter 3,we use the relative order to study the complex oscillation theory of second-order linear differential equations.We get the growth of solutions of second-order complex linear differential equations,and improve some previous results.