Properties Of Solutions Of Higher Order Complex Linear Differential Equations

In this thesis,Nevanlinna theory is mainly applied to study the prop-erties of growth in near a singular point and function spaces of solutions of the following higher order complex linear differential equation f(k)+Ak-1(z)f(k-1)+…+A1(z)f'+Ao(z)f=F(z),(1)where Aj(z)and F(z)are analytic functions,j=0,1,…,k-1.This paper includes three parts.Part 1 of the article,The Study about the properties of solutions of complex linear differential equations,We will first introduce the research background and important achievements at home and abroad,Then we review the important Nevanlinna theories and basic notation.Long-zeng[20]Obtained the estimation of[p,q]-order of solutions of the equation(1)are obtained,In this Chapter,Some estimations of[p,p+1]-order of growth of solutions of the equation are obtained,which is an extension of the Long-Zeng's results.where F(z)=0,Aj(z)(j=0,1,…,k-1)are analytic in near a singular point.By limiting coefficient of the equation(1)conditions,The growth property of the solution of the equation and its function space property are discussed,This chapter will combine the theory of complex linear differential equations with the theory of functional Spaces,We find the coefficient conditions of the equation(1)that the solution of the equation belongs to Bloch type space.