关于二阶复微分方程解的幂和解的微分多项式的不动点

本文研究了以整函数为系数的二阶线性微分方程解的幂和解生成的微分多项式的不动点问题,得到:二阶线性微分方程解生成的微分多项式的不动点性质,由于受到微分方程的限制,与一般亚纯函数的不动点性质相比是十分有趣的.事实上,它们与解的增长性密切相关.     

关于微分多项式零点的定量估计

近来有不少各种有关超越整函数或满足δ(∞,f)=1的亚纯函数f的特殊形式(微分多项式)存在有无穷多个零点或亏值的结果.本文将有些结果归结推广到对任意一超越亚纯函数的一类具广泛形式的微分多项式的零点作讨论,并得到定量的估计.在证明中用到了改进的有关微分多项式的Clunie引理并对各种辅助函数的零点重数作了较精密的估计.     

关于整函数的幅角分布

关于幅角分布的研究是亚纯函数值分布理论的一个重要分支,本文讨论了整函数结合微分多项式的幅角分布,得到了一个新的奇异方向。     

关于Frank的一个猜想

主要讨论亚纯函数与它的线性微分多项式分担三个IM值时唯一性问题,给予Frank猜想一个肯定的回答.     

线性微分多项式的有穷值点及亏量总和

证明了线性微分多项式的一个基本定理,建立了线性微分多项式对有穷值的亏量关系,这些结果是对杨乐的两个定理的推广,例子表明,本文中定理的条件是必要的。     

亚纯函数系数微分方程的解和小函数的关系

研究了一类亚纯函数为系数的二阶非齐次线性微分方程的解及其微分多项式和小函数的关系,并得到了这类微分方程解以及解的一阶,二阶导数与微分多项式的不动点性质.     

关于超越亚纯函数的一类复微分-差分多项式的零点

主要运用Nevanlinna值分布理论,研究了一类关于超越亚纯函数的复差分-微分多项式的零点问题,推广了差分-微分多项式的一些结果.利用分析函数的零点与极点的方法,证明了n取一定值时,复差分-微分多项式取零点无穷多次,结果可被看作Hayman猜想的微分-差分形式.     

整函数与其微分多项式IM分担两个值

设 f(Z)为非常数整函数 ,L (f )为 f (Z)的具有小函数系数的线性微分多项式 ,本文研究当 f(Z)与 L (f ) IM分担两个有穷复数时的唯一性问题 ,给出了 f (Z)与L (f )完全确定的表达式 ,改进了李平、杨重骏最近获得的一个结果 ,从而也改进了先前的一些结果 .     

整函数及其微分多项式分担一个多项式

将Bru¨ck猜想目前得到的几个结论进行了推广,研究了整函数及其微分多项式分担的一个多项式时的问题,并且得到了一个与之相关的复微分方程的解的性质.另外,还得到了一个定理,这个定理改进了一些已知的结果.     

权分担一个值的亚纯函数的唯一性

本文研究了亚纯函数关于微分多项式权分担一个值的唯一性问题.利用权分担值的思想,获得了一个亚纯函数唯一性定理,完善了Bhoosnurmath和Dyavanal所得的结果.     

The growth of linear differential equations and their applications

In this paper, we investigate the growth properties of solutions of linear complex differential equation and give some applications in the growth estimates of entire functions that share one finite value with one of their derivatives. This work was supported by the NNSF of China (No. 10371065) and the NSF of Shandong Province, China (No. Z2002A01).     

On the uniqueness of an entire function sharing a small entire function with some linear differential polynomial

We prove a theorem on the growth of nonconstant solutions of a linear differential equation. From this we obtain some uniqueness theorems concerning that a nonconstant entire function and its linear differential polynomial share a small entire function. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible.     

Unicity of entire functions and their linear differential polynomials

We study the relationship between an entire function f and its certain type of linear differential polynomial L when f and L share one finite nonzero value under some additional conditions. The results improve and generalize some previous results obtained by C.C. Yang and some other authors.     

A linear homogeneous partial differential equation with entire solutions represented by Bessel polynomials

We have continued our earlier studies on entire solutions of some special type linear homogeneous partial differential equations. Specifically, we deal with entire solutions of the equations that are represented in convergent series of Bessel polynomials, and determine orders and types of the solutions, in terms of their Taylor coefficients, by establishing an analogue of Lindelöf-Pringsheim theorem as well as Wiman-Valiron type theory for such functions. Finally, by using value distribution theory of holomorphic functions, we are able to exhibit some uniqueness theorems of the entire (or meromorphic) solutions.     

On meromorphic solutions of linear partial differential equations of second order

This paper is concerned with entire and meromorphic solutions of linear partial differential equations of second order with polynomial coefficients. We will characterize entire solutions for a class of partial differential equations associated with the Jacobi differential equations, and give a uniqueness theorem for their meromorphic solutions in the sense of the value distribution theory, which also applies to general linear partial differential equations of second order. The results are complemented by various examples for completeness.     

Entire functions that share one value with their linear differential polynomials

This paper studies the uniqueness problem on entire function that share a finite, nonzero value with their linear differential polynomials and proves some theorems which generalize some results given by Jank, Mues and Volkmann, P. Li, J.P. Wang and H.X. Yi.     

Entire functions that share one value CM with their derivatives

This paper studies the uniqueness problem on entire function that share a finite, nonzero value CM with their derivatives and proves two main theorems which generalize some results given by Jank, Mues and Volkmann, P. Li and C.C. Yang, H.L. Zhong etc. An example shows that the condition of one of our theorems is necessary.     

Entire functions sharing one polynomial with their derivatives

In this paper, we study the growth of solutions of ak-th order linear differential equation and that of a k + 1-th order linear differential equation. From this we affirmatively answer a uniqueness question concerning a conjecture given by Brück in 1996 under the restriction of the hyper order less than 1/2, and obtain some uniqueness theorems of a nonconstant entire function and its derivative sharing a finite nonzero complex number CM. The results in this paper also improve some known results. Some examples are provided to show that the results in this paper are best possible.     

一类高阶整函数系数线性微分方程解的超级

本文利用值分布理论,对高阶整函数系数线性微分方程(其中存在两个系数的级相等且最大)的解的复振荡性质进行了研究,得到了方程解的超级的精确估计.