二阶线性周期微分方程的解和小函数的关系

基金项目:

国家自然科学基金资助项目

详细信息

The Relation Between Solutions of Second Order Linear Differential Equations with Periodic Coefficients and Functions of Small Growth

摘要: 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.
- 小函数
Abstract: 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.
- function of small growth