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.