On Properties Of Solutions Of Complex Linear Differential Equations In The Unit Disc

In this thesis,Nevanlinna theory in the unit disc D={z:|z|<1} is mainly applied to study the properties of growth and function spaces of solutions of the following complex linear differential equation f(k)+Ak(Z)f(k-1)+…+A1(z)f’+A0(z)f=F(z),(0.0.1)where Aj(z)and F(z)are analytic functions in D,j=0,1,...,k-1.This thesis include three chapters.Firstly,the basic results and relevant notations of Nevanlinna theory in unit disc are recalled.Secondly,the research advance of the proper-ties of solutions of complex linear differential equations in unit disc is introduced in Chapter 1.Heittokangas-Korhonen-Rattya[23]obtained the general expression of solutions of the equation(0.0.1).The coefficients conditions such that the solutions of the equation(0.0.1)belong to Hardy space are characterized by combining the expression of solutions of the equation(0.0.1)with function space theory in Chapter 2.A new definition of type of meromorphic function in D was gave by Zemirni-Belaidi’s work[44].The estimation of[p,q]-order of solutions of the equation(0.0.1)are obtained by using the new definition of type in the Chapter 3,where F(z)=0.