一类高阶周期线性微分方程解的性质

On Complex Oscillation Property of Solutions for Higher-Order Periodic Differential Equations

摘要: 研究了一类高阶周期系数线性微分方程在其系数A_1起控制作用时，方程\qquad \qquad \qquad \qquad f^(k)+A_k-2f^(k-2)+\cdots+A_1f^'+A_0f=0的解f(z)和f(z+2\pi i)的线性相关性.

Abstract: The property of linearly dependence of solutions f(z) and f(z+2\pi \mathrmi) for higher-order linear differential equations f^(k)+A_k-2f^(k-2)+\cdots+A_1f^'+A_0f=0 with periodic entire coefficients is investigated, where A_1 for the equation is the dominant coefficient.