二阶线性周期微分方程的解和小函数的关系

The Relations between Solutions of Second Order Linear Differential Equations with Periodic Coefficients and Functions of Small Growth

研究了二阶线性周期微分方程f″+[P1(ez)+P2(e-z)]f'+[Q1(ez)+Q2(e-z)]f=0和f″+[P1(ez)+P2(e-z)]f'+[Q1(ez)+Q2(e-z)]f=R1(ez)+R2(e-z)的解以及它们的一阶导数、二阶导数、微分多项式与小函数之间的关系,其中P j(z)、Q j(z)及R j(z)(j=1,2)是关于z的多项式.

The relation between solutions of second order linear differential equations with periodic coefficients f″＋[P1（e^z）＋P2（e^-z）]f′＋[Q1（e^z）＋Q2（e^-z）]f=0and f″＋[P1（e^z）＋P2（e^-z）]f′＋[Q1（e^z）＋Q2（e^-z）]f=R1（e^z）＋R2（e^-z） their l th derivatives, their second derivatives, their differential polynomials with functions ofsmall growth is investigated, wherePj（z）、Qj（z）,Rj（z）（j=1,2）are polynomials.