一类亚纯函数系数的高阶齐次线性微分方程解的性质

On the Properties of Solutions of a Class of HigherOrder Homogeneous Linear Differential Equationswith Meromorphic Function Coefficents

在J.K.Langley给出的高阶齐次线性微分方程复振荡的结果的基础上,考虑具有控制系数和系数仅有有限个极点的高阶线性齐次微分方程,研究亚纯系数齐次线性微分方程亚纯解的零点收敛指数,得到了这类方程的线性无关超越解的最少个数和零点收敛指数为有穷的解的最多个数。

J.K.Langley gave several results on the complex oscillation for higher order linear differential equations,consideration has control coefficient with coefficient the high step that has limit the limit only linear in unison differential equation, we investigate the exponent of convergence of the zero-sequence of meromorphic solutions of homogeneous linear differential equations with meromorphic coefficients,Obtain the minimum number of linear independent transcendental solutions and the maximum number of linear independent transcendental solutions with finite exponents of convergence of thezero-seq uence.