ON THE GROWTH OF SOLUTIONS TO HIGHER ORDER DIFFERENTIAL EQUATION

In this paper, we consider a higher order differential equation and obtain a precise estimate of the order of growth and the hyper-order of solutions to the equation.     

高阶复线性微分方程解的角域增长性

本文研究了高阶复线性微分方程解在角域上的增长性问题.利用Nevanlinna理论和共形变换的方法,获得了一些使得方程非平凡解在角域上有快速增长的系数条件,这些结果丰富了复方程解在角域上增长性的研究.     

ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATION

In this paper, a class of higher order linear differential equation is investigated. The order and the hyper-order of the solutions of the equation are exactly estimated under some certain conditions.     

ON THE ITERATED ORDER OF MEROMORPHIC SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.     

ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATIONS

In this paper, authors investigate the order of growth and the hyper order of solutions of a class of the higher order linear differential equation, and improve results of M. Ozawa^[6], G. Gundersen^[7] and J.K. Langley^[8], Li Chun-hong^[11].     

ON THE HYPER ORDER OF SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS＊＊

The author investigates the hyper order of Solutions of the higher order linear equation, and improves the results of M. Ozawa[15], G. Gundersen[6] and J. K. Langley[12].     

ZEROS OF SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

1 Introduction and ResultsWe assume that the reader is familiar with the standard notation of Nevanlinna Theory. We use also the symbols u(f) to denote the order of ameromorphic function f, and A(f) to denote the exponent of convergence tothe zero-sequence of f.K.Ishizaki and K.TOhge studied the equationwhere pla pZ are non-constant polynomials:and Q(z) is an entire function of order less than max{n, "z}. They assumedthat cul and epZ are linearly independent and obtained in [5].Theorem A…     

关于高阶线性微分方程解的零点

本文研究了k(≥2)阶齐次线性微分方程(其中P1(z)=ξ1zn+…,P2(z)=ξ2zn+…为非常数多项式.Q1(z)(≠0),Q2(z)(≠0),Q(z),aj(z)(j=1,2,…,k一1)均为级小于n的整函数)的非平凡解f的复振荡问题,得出当ξ2-ξ1为正实数时,方程解的零点序列收敛指数的一些结果.     

一类高阶齐次线性微分方程解的零点

本文研究一类整函数系数高阶齐次线性微分方程解的零点分布.利用Nevanlinna值分布理论,得到当系数A_(k-1)的增长性起主要支配作用时,方程f~((k))+A_(k-1)f~((k-1))+···+A_0f=0任意超越解的零点收敛指数为无穷,推广了Langley和Bank等人的结果.     

复域高阶线性微分方程解的某些振荡结果

本文研究了线性微分方程解的增长性.运用值分布理论,得到方程解的增长的精确估计.进一步,讨论了上述方程解以及解的一阶,二阶导数与小函数的关系.     

HYPER ORDER OF SOLUTIONS TO SOME LINEAR DIFFERENTIAL EQUATIONS IN THE UNIT DISC

In this paper, we investigate the growth of solutions to some linear diferential equations with analytic coefcients in the unit disc. When the coefcients of these equations have some special properties near a point on the boundary of the unit disc, the order and the hyper order of the solutions to these equations are estimated accurately. Especially, our conditions on the coefcients are more general and the results on the hyper order of the solutions are new to some extent.     

几类高阶微分方程解的复振荡

本文研究了几类高阶线性微分方程解的增长性,零点,以及构成基础解的一组线形无关解的乘积的增长性.得到了5个定理,推广了陈宗煊,S.Bank和J.Langley给出的结果.     

关于高阶整函数系数微分方程解的超级

研究两种类型的高阶线性齐次整函数系数微分方程解的增长性问题。对于这两种类型的方程,当存在某个系数对方程的解的性质起主要支配作用时,得到了方程解的超级的估计,特别是对零点收敛指数是有穷的解,得到了解的超级的精确估计。     

ON OSCILLATION THEOREMS. FOR HIGHER ORDER DIFFERENTIAL EQUATIONS

In this paper,we investigate the complex oscillation of the differential equation f^(k) Ak-1f^(k-1)… A1f^1 A0f=F(x) where Af(j=0,…,k-1)F 0 are finite order entire functions. And we give precise estimates of the exponent of convergence of the zero-sequence of solutions for the above equation under some additional hypotheses.     

ON THE GROWTH OF SOLUTIONS OF HIGHER-ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS

Using Nevanlinna theory of the value distribution of meromorphic functions, the author investigates the problem of the growth of solutions of two types of algebraic differential equation and obtains some results.     

高阶代数微分方程解的增长级(英文)

本文研究了高阶代数微分方程解的增长级的问题.利用亚纯函数的Nevanlinna值分布理论和微分方程的一些技巧,得到了一个更精确和更一般的结论,推广了何育赞和Laine的一些理论.     

一类高阶线性微分方程解的复振荡性质

本文研究一类高阶线性齐次与非齐次迭代级整函数系数微分方程解的增长性问题.当存在某个系数或自由项对方程解的性质起主要支配作用时,得到了方程解的迭代级及其零点的迭代收敛指数的精确估计,推广了已有的结果.     

二阶代数微分方程亚纯解的增长性估计

本文研究了代数微分方程亚纯解的增长级.运用正规族理论,给出了某类二阶代数微分方程亚纯解的增长级的一个估计,该估计依赖于方程的有理函数系数.推广了2001年廖良文与杨重骏的一个结果.