The Growth of Solutions of Higher Order Differential Equations with Coefficients Having the Same Order

被引：0

作者：

Yanyan ZHAN ^{[1
]}

Lipeng XIAO ^{[1
]}

机构：

[1] College of Mathematics and Information Science,Jiangxi Normal University

来源：

Journal of Mathematical Research with Applications | 2015年 / 35卷 / 04期

基金：

中国国家自然科学基金;

关键词：

order of growth; hyper-order; exponent of convergence of zero sequence; differential equation;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

In this paper,we consider the growth of solutions of some homogeneous and nonhomogeneous higher order differential equations.It is proved that under some conditions for entire functions F,A;and polynomials P;（z）,Q;（z）(j=0,1,…,k-1;i=1,2)with degree n≥1,the equation f;+(A;（z）e;p;（z）)+A;（z）e;Q;)/;+…+(A;（z）e;+A;（z）e;)f=F,where k≥2,satisfies the properties:When F ≡0,all the non-zero solutions are of infinite order;when F=0,there exists at most one exceptional solution fo with finite order,and all other solutions satisfy λ（f）=λ（f）=σ（f）=∞.

引用

页码：387 / 399

页数：13

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