二阶线性周期微分方程的解和小函数的关系
The Relation Between Solutions of Second Order Linear Differential Equations with Periodic Coefficients and Functions of Small Growth
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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.Abstract: The relation between solutions of second order linear differential equations with periodic coefficientsf^\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.
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