The Property Of Solutions Of Complex Linear Differential Equations

In this paper,we nainly use t he t heory of differential equat i on,Nevanlinna theory to study the growth of the solution of second order linear differential equations in the whole conplex plane,and consider the property of solutions of higher order linear differential equation in the unitdisc D.There are three parts in this paper.In part one,we give a brief introduction of the devel opnennt history of this research fied and introduce the nain result in this paper.In part two,we introduce sonerel at ed definitions,signs, nany related lenmas and conside the growth of solutions of second order linear differential equation.f"+A(z)f’+B(z)f=0, where A(z)=αnenz+αn-1(n-1)z＋…+α1ez+α0/bmemz+bm-1e(m-1)z+…+b1ez+b0,B(z) is an entire transcendental function of finite order ρ(B)≠1.Then every nontrivial solutions f(z) of the equation has infinite order.In part three,we nainly consi der hi gher linear differential equation f(k)+Ak-1(z)f(k-1)+…+A1(z)f’+A0(z)f=0,when coefficient A1(z) satisfies sone conditions,then all solutions belong to Betslogp,q,m space.