二阶线性周期微分方程的解和小函数的关系

研究了二阶线性周期微分方程$f^{\prime\prime}+P_1(e^{z})+P_2(e^{-z})]f^{\prime}+Q_1(e^{z})+Q_2(e^{-z})]f=0$和$f^{\prime\prime}+P_1(e^{z})+P_2(e^{-z})]f^{\prime}+Q_1(e^{z})+Q_2(e^{-z})]f=R_1(e^{z})+R_2(e^{-z})$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$P_j(z)$和$Q_j(z)$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 and Functions of Small Growth

The relation between solutions of second order linear differential equations with periodic coefficients$f^{\prime\prime}+P_1(e^{z})+P_2(e^{-z})]f^{\prime}+Q_1(e^{z})+Q_2(e^{-z})]f=0$ and $f^{\prime\prime}+P_1(e^{z})+P_2(e^{-z})]f^{\prime}+Q_1(e^{z})+Q_2(e^{-z})]f=R_1(e^{z})+R_2(e^{-z})$,their 1th derivatives, their second derivatives, their differential polynomials with functions of small growth is investigated, where $P_j(z),~ Q_j(z),R_j(z)$(j=1,2) are polynomials.