摘要
本文研究了非齐次线性微分方程ｆ（ｋ） ＋ Ｄｋ－ １ｆ（ｋ－ １） ＋ …＋ Ｄ０ｆ ＝ Ｆ （１）的复振荡问题．其中Ｄ０，…，Ｄｋ－ １是增长级小于１／２的亚纯函数，Ｆ０是有限级亚纯函数．当存在某个ＤＳ（０≤ｓ≤ｋ－ １）比其它Ｄｊ（ｊ≠ｓ）有较快增长的意义下起支配作用时，得到了微分方程（Ⅰ）的一定条件下亚纯解的级和零点的估计式．
In this paper, we investigate the complex oscillation of the differential equationf (k) +D k-1 f (k-1) +…+D 0f=F(1)where D 0, …, D k-1 are meromorphic functions with the order of growth smaller than 1/2, F 0 is a meromorphic function with finite order of growth, and there exists a D s(0≤s≤k-1) being dominant in the sense that it has larger growth than D j(j≠s) . Under certain conditions, we obtain some estimates of the exponent of convergence of the zero sequence and the order of growth of meromorphic solution of equation (1).
出处
《数学杂志》
CSCD
1999年第4期371-376,共6页
Journal of Mathematics
关键词
非齐次
线性
微分方程
级
极点
零点
亚纯解
nonhomogeneous differential equation
order
lower order
pole
zero
