复高阶差分方程解

利用亚纯函数的Nevanlinna值分布理论,讨论了两类复高阶差分方程亚纯解的存在性和增长级问题,一类复差分方程的Malmquist型定理被建立,另一类复差分方程解的增长级得到估计.例子表明了我们的结果是精确的.     

某些差分多项式的亏量

Halburd和Korhonen指出研究复域差分的值分布问题对进一步研究复域差分与差分方程具有十分重要的意义.本文得到了关于有限级亚纯函数的差分多项式的亏量为一些结果,其中部分结果可视为微分多项式相应结果的差分模拟.同时,我们在一定条件下给出了经典的Valiron-Mohon'ko定理的一个差分模拟结果,并且作为本文中的一个重要工具出现.这些结果推广了前人已有结果.     

一些差分-复合函数方程的亚纯解

利用Nevanlinna值分布理论,我们主要讨论了两类复差分-复合函数方程和一类复差分-复合函数方程组的超越亚纯解的存在性和特征估计,得到了几个结果.一些例子表明了定理中的条件是精确的.     

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.     

具有代数体函数解的一类复常微分方程

本文应用Nevanlinna理论,研究了一类相当一般的复常微分方程的代数体函数解的存在性问题并得到若干新的结果。一、引言微分方程代数体函数解的存在性问题,首先由Malmquist所研究,吉田耕作首先应用Nevanlinna理论的方法重新证明和推广了Malmquist定理,其后,F. Gackstatter和I. Laine;何育赞与肖修治考虑了下述微分方程的相应问题:     

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.     

一类复微分-差分方程的亚纯解（英文）

本文研究一类复微分-差分方程的亚纯解的性质和表达式问题,利用亚纯函数的Nevanlinna值分布理论来证明,并得到一些结论,所得结论是从复差分方程到复微分差分方程的推广.例子表明我们的结果是有意义的.     

关于一类复差分方程的亚纯解

研究了具有允许的亚纯解的复差分方程的形式以及系数的级与解的级两者的关系,得到了两个结果.将复微分方程中一些结果推广至复差分方程.     

亚纯函数差分多项式的值分布

本文讨论了差分多项式的特征函数和零点. 特别地, 本文将Valiron-Mohon''ko 定理部分地推广到了差分多项式, 并且对微分多项式零点的一些经典结果建立了差分模拟.     

二阶差分边值问题的正解

本文研究了非线性项具有半正定和混合单调性的二阶差分边值问题正解的存在性.利用Krasnosel'skii不动点定理和锥拉伸与锥压缩不动点定理,讨论了二阶半正定非线性差分边值问题以及非线性项具有半正定和混合单调性的特征值问题正解的存在性,给出了这几类差分边值问题的正解存在性定理,改进和推广了具有正定非线性项的二阶差分边值问题的一些结果,并将所得结果应用于一个具体的二阶半正定非线性差分边值问题中.     

一类高阶偏微分方程的亚纯解

利用多复变值分布理论,我们将Steinmetz的代数微分方程的Malmqiust型定理推广到复偏微分方程中．     

Cm 中高阶偏微分方程的代数体解

该文利用多复变函数值分布理论和技巧, 研究了C^m中高阶偏微分方程的代数体函数解的存在性问题, 建立了C^m中高阶偏微分方程的Malmquist型定理.     

On existence of solutions of differential‐difference equations

This paper applies Nevanlinna theory of value distribution to discuss existence of solutions of certain types of non‐linear differential‐difference equations such as (5) and (8) given in the succeeding paragraphs. Existence of solutions of differential equations and difference equations can be said to have been well studied, that of differential‐difference equations, on the other hand, have been paid little attention. Such mixed type equations have great significance in applications. This paper, in particular, generalizes the Rellich–Wittich‐type theorem and Malmquist‐type theorem about differential equations to the case of differential‐difference equations. Copyright © 2015 John Wiley & Sons, Ltd.     

Further results on factorization of meromorphic solutions of partial differential equations

This paper is a continuation of Hu-Yang [2]. Here we extend Malmquist type theorem ofalgebraic differential equations of Steinmetz [3] and Tu [4] to higher order partial differential equations. The results also generalize Theorems 4.2 and 4.3 in [2].     

Entire solutions of delay differential equations of Malmquist type

The celebrated Malmquist theorem states that a differential equation, which admits a transcendental meromorphic solution, reduces into a Riccati differential equation. Motivated by the integrability of difference equations, this paper investigates the delay differential equations of form $w(z+1)-w(z-1)+a(z)\frac{w''(z)}{w(z)}=R(z, w(z))(*),$ where $R(z, w(z))$ is an irreducible rational function in $w(z)$ with rational coefficients and $a(z)$ is a rational function. We characterize all reduced forms when the equation $(*)$ admits a transcendental entire solution with hyper-order less than one. When we compare with the results obtained by Halburd and Korhonen[Proc. Amer. Math. Soc. 145, no.6 (2017)], we obtain the reduced forms without the assumptions that the denominator of rational function $R(z,w(z))$ has roots that are nonzero rational functions in $z$. The value distribution and forms of transcendental entire solutions for the reduced delay differential equations are studied. The existence of finite iterated order entire solutions of the Kac-van Moerbeke delay differential equation is also detected.     

Asymptotic behavior of solutions of functional difference equations

For linear functional difference equations, we obtain some results on the asymptotic behavior of solutions, which correspond to a Perron-type theorem for linear ordinary difference equations. We also apply our results to Volterra difference equations with infinite delay.     

Preservation of stability under discretization of systems of ordinary differential equations

We study the stability preservation problem while passing from ordinary differential to difference equations. Using the method of Lyapunov functions, we determine the conditions under which the asymptotic stability of the zero solutions to systems of differential equations implies that the zero solutions to the corresponding difference systems are asymptotically stable as well. We prove a theorem on the stability of perturbed systems, estimate the duration of transition processes for some class of systems of nonlinear difference equations, and study the conditions of the stability of complex systems in nonlinear approximation.     

Basic Theory of Fuzzy Difference Equations

The notion of fuzzy difference equation is introduced. Using Lyapunov type of function a comparison theorem for the fuzzy difference equation is obtained in terms of ordinary difference equations, which is used as a tool to study the stability results of the fuzzy difference equations.     

Fixed points of a mapping and Hyers–Ulam stability

We show that many general results on Hyers–Ulam stability of some functional equations in a single variable follow immediately from a simple fixed point theorem. The theorem is formulated for self-maps of some subsets of the space of functions from a nonempty set into the set of reals. We also give some applications of that theorem, e.g., in investigations of solutions of some difference equations and functional inequalities.     

一类高阶代数微分方程的亚纯允许解

利用亚纯函数的Nevanlinna值分布理论,研究了一类高阶微分方程具有亚纯允许解时,它所具有的形式,得到了一个Malmquist型定理。