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关于超越亚纯系数微分方程亚纯解的零点
引用本文:陈宗煊.关于超越亚纯系数微分方程亚纯解的零点[J].系统科学与数学,1997,17(2):148-155.
作者姓名:陈宗煊
作者单位:江西师范大学数学系!南昌,330027
基金项目:国家自然科学基金,江西省自然科学基金
摘    要:本文研究了非齐次线性微分方程的复振荡问题,其中,D0,D1,…,D(k-1),是超越亚纯函数.当存在某个Ds(1≤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)亚纯解的零点收敛指数的精确估计式.

关 键 词:线性微分方程  亚纯函数  零点  收敛指数

ON THE ZEROS OF MEROMORPHIC SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH TRANSCENDENTAL MEROMORPHIC COEFFICIENTS
Zong Xuan CHEN.ON THE ZEROS OF MEROMORPHIC SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH TRANSCENDENTAL MEROMORPHIC COEFFICIENTS[J].Journal of Systems Science and Mathematical Sciences,1997,17(2):148-155.
Authors:Zong Xuan CHEN
Institution:Department Mathematics, Jiangxi Normal University, Nanchang, 330027
Abstract:In this paper, we investigate the complex oscillation of the differential equation $$ f^{(k)}+D_{k-1}f^{(k-1)}+\cdots+ D_0f=F,\eqno{(I)} $$ where $D_0,D_1,\cdots,D_{k-1}$, $F\neq 0$ are transcendental meromorphic functions. When there existsa $D_s(1\leq s\leq k-1)$ being dominant in the sense that it has larger growth than any other $D_j(j\neq s)$, we obtain some precise estimates of the exponent of convergence of the zero-sequence of meromorphic solutions for the above equation.
Keywords:Linear differential equation  meromorphic function  zero  exponent of convergence  
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