Some Properties of Solutions of Periodic Second Order Linear Differential Equations

DOI：10.3770/j.issn:1000-341X.2011.02.011

 作者 单位 肖丽鹏 江西师范大学数学与信息科学学院, 江西 南昌 330022 陈宗煊 华南师范大学数学科学学院, 广东 广州 510631

在本文中，我们研究了二阶周期线性微分方程$$y'' Ay=0,$$解的零点，其中$A(z)=B(e^z), B(\zeta)=g(\zeta) \sum_{j=1}^pb_{-j}\zeta^{-j}, g(\zeta)$是一超越整函数满足下级不超过1/2，p是一正的奇数。我们得到的结果是上述方程的每一个非平凡解的零点收敛指数为无穷。

In this paper, the zeros of solutions of periodic second order linear differential equation $y'' Ay=0$, where $A(z)=B(e^z)$, $B(\zeta)=g(\zeta) \sum_{j=1}^pb_{-j}\zeta^{-j}$, $g(\zeta)$ is a transcendental entire function of lower order no more than $1/2$, and $p$ is an odd positive integer, are studied. It is shown that every non-trivial solution of above equation satisfies the exponent of convergence of zeros equals to infinity.