摘要
考虑二阶方程 f″ +(B1(z)eP1(z) +B2 (z)eP2 (z) +Q(x) ) f =0 ,其中P1(z) =ζ1zn+… ,P2 (z) =ζ2 zn+… (ζ1ζ2 ≠ 0 )为非常数多项式 ,B1(z) 0 ,B2 (z) 0 ,Q(z)为级小于n的整函数 ,得到如下结果 :若 ζ1/ ζ2 不是实数 ,则上述微分方程的任一非平凡解的零点收敛指数为∞ .
In this paper,we consider the second order differential equation f″+(B 1(z)e P 1(z) + B 2(z)e P 2(z) +Q(z))f=0,where P 1(z)=ζ 1z n+…,P 2(z)=ζ 2z n+…(ζ 1ζ 2≠0) are non constant polynomials,B 1(z)0,B 2(z)0,Q(z) are entire functions and their orders are less than n.We obtain the following result:if ζ 1/ζ 2 is non real,then the exponent of convergence of the zero sequence of any non trivial solution of the above equation is ∞.
出处
《江西师范大学学报（自然科学版）》
CAS
2000年第1期28-33,44,共7页
Journal of Jiangxi Normal University(Natural Science Edition)
基金
国家自然科学基金资助项目!(1976 10 0 2 )
关键词
二阶微分方程
整函数
复振荡
解
线性
second order differential equation
entire function
complex oscillation
