二阶周期线性微分方程解的几个性质

Some Properties of Solutions of Periodic Second Order Linear Differential Equations

中文关键词:  周期微分方程  复振荡  正则增长级.

英文关键词:periodic differential equation  complex oscillation  regular order of growth.

中文摘要:

      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。

英文摘要:

      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.