周期系数高阶线性微分方程的次正规解

Subnormal Solutions of higher Order Linear Differential Equations with Periodic Coefficients

摘要: 考虑周期系数高阶线性微分方程 f^(n)+\sum\limits_j=1^nP_n-j (e^z)+ Q_n-j (e^-z) f^(n-j) = R_1(e^z) + R_2 (e^-z), 其中 n\geq 2, P_j (z), Q_j (z)(j=0,1,2,\cdots, n-1), R_1(z) 和 R_2(z) 均是关于 z 的多项式, 且 P_j (z), Q_j (z) (j=0,1,2,\cdots, n-1) 不全为常数. 在条件 \deg P_j\deg P_0 ,(j=1,2,\cdots, n-1) 下, 获得方程的次正规解的表示.

Abstract: The representations of subnormal solutions for the higher order linear differential equation f^(n)+\sum\limits_j=1^nP_n-j (\mathrme^z)+ Q_n-j (\mathrme^-z) f^(n-j) = R_1(\mathrme^z) + R_2 (\mathrme^-z) are obtained, where n\geq 2, P_j (z), Q_j (z)(j=0,1,2,\cdots, n-1), R_1(z) and R_2(z) are polynomials in z such that P_j (z), Q_j (z) (j=0,1,2,\cdots, n-1) are not all constants, and \deg P_j\deg P_0 ,(j=1,2,\cdots, n-1).