Meromorphic solutions of some types of complex differential-difference equations

Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some properties of meromorphic solutions, and we obtain some results, which are the improvements and extensions of some results in references. Examples show that our results are precise.     

On some results of Yi and their applications in the functional equations

In this article, we establish some uniqueness theorems that improves some results of H. X. Yi for a family of meromorphic functions, and as applications, we give some results about the non-existence of meromorphic solutions of Fermat type functional equations.     

与其导数具有分担值的亚纯函数唯一性

为进一步丰富亚纯函数唯一性理论,寻求更佳的唯一性条件,利用亚纯函数Nevanlinna理论更精确地估计亚纯函数的n重值点的计数函数,得到两个亚纯函数与其导数具有某些分担值时的唯一性定理,推广和改进了相关文献的相关结果.     

二阶代数微分方程超越亚纯解

Using Nevanlinna theory of the value distribution of meromorphic functions,we discuss some properties of the transcendental meromorphic solutions of second-order algebraic differential equations,and generalize some results of some authors.     

关于某类Briot-Bouquet微分方程若干结果的推广

本文研究了某类形式的Briot-Bouquet微分方程的亚纯解结构问题.利用Nevanlinna值分布理论的有关知识,获得了该类微分方程的所有可能形式,以及当方程的阶为偶数时,给出了每一个形式的方程的亚纯解结构,推广了某些特定的Briot-Bouquet微分方程亚纯解结构的一些结果.     

On normal families of meromorphic functions

In this paper, we study the normality of a family of meromorphic functions and obtain some normality results for meromorphic functions, which improve and generalize the related results of Gu, Bergweiler and Lin.     

RICCATI-TYPE RESULT FOR MEROMORPHIC SOLUTIONS OF SYSTEMS OF COMPOSITE FUNCTIONAL EQUATIONS

By use of Nevanlinna value distribution theory,we will investigate the properties of meromorphic solutions of two types of systems of composite functional equations and obtain some results. One of the results we get is about both components of meromorphic solutions on the system of composite functional equations satisfying Riccati differential equation,the other one is property of meromorphic solutions of the other system of composite functional equations while restricting the growth.     

亚纯函数族的几个正规定则

研究了亚纯函数族的正规族问题.利用Zalcman引理的方法,获得了亚纯函数族的几个正规定则.并改进了相关文献的结论.     

Expression of meromorphic solutions of systems of algebraic differential equations with exponential coefficients

Using the Nevanlinna theory of the value distribution of meromorphic functions and theory of differential algebra, we investigate the problem of the forms of meromorphic solutions of some specific systems of generalized higher order algebraic differential equations with exponential coefficients and obtain some results.     

关于高阶代数微分方程组亚纯解的计数函数（英文）

Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equations and obtain some results.     

关于亚纯函数唯一性的一些结果

本文研究了涉及重值的具有四个公共小函数的亚纯函数的唯一性问题.利用关于小函数的Nevanlinna第二基本定理精简形式及处理小函数的有关方法,改进了有关结果.利用Gundersen处理公共值对的方法,对具有五个IM公共值对和四个IM公共小函数对的亚纯函数的情况作了进一步讨论,推广改进了相关结果.     

一类复差分方程组的亚纯解

许多作者研究了复差分方程解的存在性及增长性问题,得到了较多理想的结果.本文利用亚纯函数Nevanlinna值分布理论,研究了一类复高阶非线性差分方程解的表达式问题,将复差分方程的一结果推广至复差分方程组中.     

关于亚纯函数的正规族

在本文研究了亚纯函数族的正规族问题,利用Zalcman引理的方法,获得了亚纯函数族的几个正规定则.并改进了顾永兴和Bergweiler的结果.     

Weighted value sharing and a question of I. Lahiri

In this article, we investigate the problem due to I. Lahiri [I. Lahiri (2001). Weighted value sharing and uniqueness of meromorphic functions. Complex Variables Theory Appl., 46, 241–253.]. Also we prove some uniqueness theorems of meromorphic functions which improve some earlier results.     

ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH SHARED-SETS IN AN ANGULAR DOMAIN

In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.     

一类高阶微分方程亚纯解的增长性

研究了几种类型的高阶线性亚纯系数微分方程的亚纯解的增长性,对方程的亚纯解的增长率得到了精确估计.     

某些常微分方程的亚纯解表示与应用

本文运用Nevanlinna值分布理论研究了某些常微分方程亚纯解的存在性. 对于某些具有控制项的常系数常微分方程, 本文得到了亚纯解的表示, 并且给出了求相应偏微分方程精确解的一种方法.作为例子, 本文运用此方法得到了著名的KdV方程的所有亚纯行波精确解. 结果显示该方法比其他方法简单.     

On growth of meromorphic solutions of some kind of non-homogeneous linear difference equations

In this paper, we investigate the growth of meromorphic solutions of some kind of non-homogeneous linear difference equations with special meromorphic coefficients. When there are more than one coefficient having the same maximal order and the same maximal type, the estimates on the lower bound of the order of meromorphic solutions of the involved equations are obtained. Meanwhile, the above estimates are sharpened by combining the relative results of the corresponding homogeneous linear difference equations.     

涉及移动目标的亚纯映射唯一性定理

本文首先证明了一个新的从C~n到P~N(C)的亚纯映射第二基本定理,其中涉及到带有不同权重的截断型计算函数;其次利用这个新的第二基本定理,考虑了退化的亚纯映射在分担处于一般位置的移动超平面下的唯一性问题,并在较弱的条件下获得了一个唯一性结果,改进了已有的一些经典结果.     

一类复差分方程组的亚纯解(英文)

本文研究了一类复差分方程组的增长性的问题.利用亚纯函数的Nevanlinna值分布理论,得到了有关复差分方程组的亚纯解的一个重要结果,将复差分方程的某些结果推广到复差分方程组中.