复微分-差分方程组的超越整函数解

利用亚纯函数的Nevanlinna值分布理论, 我们主要研究了一类复微分-差分方程和一类复微分-差分方程组的有限级超越整函数解的存在形式, 得到两个有趣的结论. 将复微分(差分)方程的一些结论推广到复微分-差分方程(组)中.     

Fermat型复微分-差分方程的整函数解北大核心CSCD

利用值分布理论,研究了一类Fermat型复微分-差分方程与复微分-差分方程组,得到有限级超越整函数解的存在条件与具体形式,推广改进了高凌云、刘凯、曾翠萍等人的结果.     

复微分-差分方程组的整函数解

利用值分布理论,研究了一类n阶复微分-差分方程ω~(n)(z)~2+[αω(z+c)-βω(z)]~2=1和复微分-差分方程组■是否存在有限级整函数解的问题.本文推广并改进了高凌云和刘凯等人的结果.     

关于一类复微分-差分方程组的解

作者主要研究了一类复微分-差分方程组的有限级整函数解,得到了一有趣的结果,将复微分(或差分)方程中相关结果推广至复微分-差分方程组中.     

复微分-差分方程组的超越解 献给余家荣教授100华诞

本文利用复差分值分布理论和复微分方程理论,将复差分方程和微分方程结合起来,首先研究一类复高阶微分-差分方程超越整函数解,给出其超越整函数解的具体形式.其次,进一步考虑更为复杂的两类复微分-差分方程组超越整函数解的形式以及微分-差分方程组解的存在性问题,得到在一定条件下不存在超越整函数解的结论,例子表明本文定理中的条件是精确的.第三,讨论一类复微分-差分方程组,得到关于解的增长级的一个结果.最后,讨论一类复高阶?差分微分-函数方程超越亚纯解的特征函数,在对其系数的特征函数给出限制时,得到其超越亚纯解的特征估计,例子也表明本文的条件是精确的.     

关于复差分方程组的允许解的形式

利用亚纯函数的值分布理论,该文主要研究了复差分方程组的允许解的形式,得到一个结论,将复微分(差分)方程的相关结论推广到复差分方程组中,例子表明该文结论精确.     

一类复差分方程组的亚纯解（英文）

文中利用亚纯函数Nevanlina理论和复差分理论,研究一类复差分方程组有限级非亚纯允许解的存在性问题.同时,讨论了这类复差分方程组存在有限级亚纯允许解时方程组的形式.     

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.     

关于复差分微分理论的若干结果

本文主要利用差分的Nevanlinna理论,研究了几种不同类型的复差分微分多项式的零点情况,推广了微分多项式理论中的一些经典结果,同时也推广了部分差分多项式的结果.另外,本文还得到了某些差分微分方程解的存在性.     

On entire solutions of two types of systems of complex differential-difference equations

In this paper, we will mainly investigate entire solutions with finite order of two types of systems of differential-difference equations, and obtain some interesting results. It extends some results concerning complex differential (difference) equations to the systems of differential-difference equations.     

复微分方程组及复微分-差分方程解的级

利用Zalcman关于正规族的方法,研究了两类复高阶微分方程组的亚纯解的增长级问题;同时,利用Nevanlinna值分布理论,讨论了两类复微分-差分方程的超越整函数解的增长级.所得结论推广和改进了一些文献的结果,并举例说明本文的结论精确.     

微分、差分方程的机械化方法

介绍了微分与差分方程机械化方法研究若干最新进展.主要结果包括: 微分、差分方程的特征列理论与算法,微分、差分方程系统的分解算法以及微分、差分方程解析解求解算法.     

Some Properties of Meromorphic Solutions to Systems of Complex Differential-Difference Equations

Applying Nevanlinna theory of the value distribution of meromorphic functions, the author studies some properties of Nevanlinna counting function and proximity function of meromorphic solutions to a type of systems of complex differential-difference equations. Specifically speaking, the estimates about counting function and proximity function of meromorphic solutions to systems of complex differential-difference equations can be given.     

差分方程拉克斯对的一种构造性方法

非交换微分在讨论数学物理中的偏微分方程时起着十分重要的作用.最近,作者利用一个具体的非交换外微分建立了一种求差分微分方程拉克斯对的方法,由此检验了该方程的可积性.本文给出了讨论全差分方程的对应理论.另外还讨论了一个格子形变的KdV(LMKdV)方程,并求得了它的拉克斯对.     

Basis difference method for orthogonal systems on a surface

The basis operator method intended for constructing systems of difference approximations to differential operators in vector and tensor analysis is extended to orthogonal systems on a surface. A class of completely conservative differential-difference schemes for continuum mechanics in Lagrangian variables is constructed. Basis operators are constructed using the finite volume equation, consistency conditions for discrete operators of the first derivative, and consistent projection operators for grid functions. A system of differential-difference continuum mechanics equations on a surface is obtained, which implies all conservation laws typical of the continuum case, including additional ones. A stability estimate is derived for discrete equations of an incompressible viscous fluid.     

Malmquist型复差分方程组

近来一些论文里,Ablowitz,Halburd以及Herbst等人应用Nevanlinna理论证明了类似于复微分方程Malmquist定理的复差分方程一些结果.本文主要研究一类复差分方程组的Malmquist定理,推广和改进了他们的一些结论.     

Periodic solutions for coupled systems of differential-difference and difference equations

Summary The objective of this paper is to give necessary and sufficient conditions for the existence of periodic solutions of coupled systems of differential-difference and difference equations. By differentiating the difference equation, we obtain a system of neutral differential-difference equations and we get the original problem by putting a side condition on the neutral equation; that is, by restricting the initial data to lie on certain manifold in the space of all initial data. This allows us to treat the problem using the methods of neutral functional differential equations. In[8], Hale and Martinez-Amore exploited a certain change of variables to obtain some results on the stability of this systems. In Section 2, we summarize those ideas. The effect of the side condition is reflected in the variation of constants formula in Section 3. In this section, the variation of constants formula is decomposed via eigenspaces. In Section 4, we give a theorem on the Fredholm alternative for periodic solutions which is basic to the application of the usual theory to perturbed linear problems. I want to express my most deep gratitude to Professor J. K. Hale for his advice and suggestions which led to considerable improvements of this paper. Entrata in Redazione l'8 marzo 1978. Research was supported in the form of Grant from the Program of Cultural Exchange between the United States and Spain.