ON MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF COMPOSITE FUNCTIONAL EQUATIONS

In this article,we mainly investigate the growth and existence of meromorphic solutions of a type of systems of composite functional equations,and obtain some interesting results.It extends some result...     

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.     

复线性微分方程解的增长性的几个结果

本文研究了复线性微分方程解的增长性问题.利用两类具有某种渐进增长性质的函数作为线性微分方程的系数,讨论了两类二阶线性微分方程解的增长性,获得了方程解为无穷级.这些结果推广了先前的一些结果.     

复代数微分方程的代数体允许解的一些结果

我们讨论了复代数微分方程的代数体允许解的存在性问题,得到了一些结果.例子表明了定理中的上界是可以达到的.     

一类复函数方程组的亚纯解

本文研究了一类复函数方程组的亚纯解的存在性问题.利用亚纯函数的Nevanlinna值分布理论,得到了有关方程组的亚纯解变成了有理解的一个主要结论,将复函数方程的某些结果推广至复函数方程组中.     

函数方程组的亚纯解(英文)

本文主要研究以下类型函数方程组亚纯解的存在性和增长性问题{f1n（cz）=a（z） (f₁^m1（z）/(f₂^m2（z）),f₂ n（cz）=b（z）(f₂（m1）^z)/(f₁^m2（z）),其中a（z）,b（z）为有理函数,|c|=0,1,n>1,mi>1（i=1,2）.利用亚纯函数的Nevanlinna值分布理论与及复函数方程研究部分方法,获得了定理1,2,3三个关于函数方程组的结果,推广了函数方程中的一些结果.     

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.     

一类泛函微分方程的稳定性定理及其应用

本文采用一种新方法来研究 RFDE 稳定性问题,其特点是不必构造 Liapunov 泛函,用起来比较简单,应用得到的稳定性定理,本文还研究了许多领域中有重要意义的Volterra 积分微分方程的周期解的唯一性和稳定性问题.     

Markov骨架过程积分型泛函的分布和矩及其应用举例

侯振挺等^[1]引入了一类具有广泛应用前景的随机过程－Markov骨架过程,本文研究这类过程积分型泛函的分布和矩及其计算问题,作为应用,我们得到了Doob过程,生灰2过程积分型泛函的分布和矩的公式,尤其对于生灭过程,利用本文的方法也得到了[4]中定理1－3的结果。     

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.     

MULTIVALUED DIFFERENTIAL EQUATIONS IN BANACH SPACES AND THEIR APPLICATIONS

IIntroductionConsider the initial value problemDtL干Au＋1ugi．U＜t＜I,oh山)”w,where A is of of。s(S＋)and F is a multivalued msp．If F is singl。vlued Hiranoti goteistence results for Fbeing compact．Ahmed and Xiang[21 extended Hirano’s results forFsatls州ngthat＜Fu。,u。一U＞－＋ 0 lfunconverges wewyto h;While Liul3]e枕ended theabOV6 th6lltlollsd T6SllltS to COf正erpolldlllg ClAsS Of yatlatlollal ill6qttallt16s ld lfittodllC6d 8 hO16gmerdC0nd让ND th幼劝m比a bro劝0 d%sdpenurb砒…     

THEORY AND APPLICATIONS OF MONOTONE SEMIFLOWS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS

The theory of monotone semiflows has been widely applied to functional differential equations (FDEs). The studies on the theory and applications of monotone semiflows for FDEs are very important and interesting. A brief des-cription of our recent works are as follows.By using general monotone semiflow theory, several results of positively invariant sets, monotone solutions and contracting rectangles of retarded functional differential equations(RFDEs) with infinite delay are gained under the assumption of quasimonotonicity; sufficient conditions for the existence, un-iqueness and global attractivity of periodic solutions are also established by combining the theory of monotone semiflows for neutral functional differential equations(NFDEs) and Krasnoselskii's fixed point theorem.     

一类中立型泛函微分方程周期解问题

本文利用Ｆｏｕｒｉｅｒ级数理论和不动点原理研究了一类中立型泛函微分方程（ＮＦＤＥＳ）：（ｄ／ｄｔ）∫「ｄＤ（ｓ）」ｘ（ｔ＋ｓ）＝∫ｒ「ＤＬ（ｓ）」ｘ（ｔ＋ｓ）＋Ｎｘ（ｔ）的周期解问题,得到了解的存在性和唯一性的新结果,所得结果推广和改进了文「５」的工作。     

论筛法及其有关的若干应用——殆素数的分布问题

<正> 本文的宗旨在于证明作者在[1]内所提及的全部结果,现在将本文的强果详述于下:定理1.命 F(x)表一无固定素因子的 k 次既约整值多项式.命(?)此处 w 是适合下面不等式的最小正整数(?)则在叙列{F(x)}中存在无限多个不超过 n 个素数的乘积.例如存在无限多个 x,使 x~3+2的素因子个数(包括相同的与相异的)不多于4.与此相类似,有定理2.设 k 为一正整数,命 n 适合(1)及(2),则当 x 充分大时,区间 x相似文献   

UNIQUENESS AND VALUE DISTRIBUTION ON DIFFERENCE POLYNOMIALS OF MEROMORPHIC FUNCTIONS

In this paper, we study the value distribution question of certain difference polynomials of meromorphic functions, and investigate the uniqueness questions of meromorphic functions whose certain difference polynomials share a small functions. The results in this paper improve and extend the corresponding results in Zhang [16] and Chen [1].     

含随机参数非线性方程组解的存在性、唯一性及算法与效用函数计算公式的导出

1 引 言在决策分析及若干非确定性经济分析中,如何确定行为人效用函数及其计算公式,是迄今仍未解决的重大问题.近些年有多项研究均涉及此问题[1,2,3,4].Multiple Degree RiskAversion模型[5,6],可通过鉴别行为人风险性质,把上述效用函数及其参数的确定归结为求解由所定义函数构造的一种非线性方程组.这里,用途最广也最具代表性的风险性质为递减风险厌恶[7].其效用函数及其参数可由关于未知量ψ1,ψ2的两个联立非线性方程     

EXISTENCE AND MOMENT ESTIMATES FOR SOLUTIONS TO NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, we show the existence and uniqueness of solutions to a large class of SFDEs with the generalized local Lipschitzian coefficients. Some moment estima- tes of the solutions are given by establishing new Ito operator inequalities based on the Razumikhin technique. These estimates improve, extend and unify some related results including exponential stability of Mao （1997） [20], decay stability of Wu et al. （2010,2011） [32,33], Pavlovic et al. （2012） [24], asymptotic behavior of Luo et al. （2011） [18] and Song et al. （2013） [26]. Moreover, stochastic version of Wintner theorem in continuous space is established by the comparison principle, which improve and extend the main results of Xu et al. （2008 [39], 2013 [36]）. When the methods presented are applied to the SFDEs with impulses and SFDEs in Hilbert spaces, we extend the related results of Govindana et al. （2013） [7], Liu et al. （2007） [15], Vinod- kumar （2010） [29] and Xu et al. （2012） [35]. Two examples are provided to illustrate the effectiveness of our results.     

泛函微分方程的Lipschitz指数稳定性

提出泛函微分方程的Lipschitz指数稳定性概念,给出了利用Liapunov泛函数研究Lipschitz指数稳定性的条件。     

DISCUSSION ON THE CONTINUOUS SOLUTIONS OF A FUNCTIONAL EQUATION

1 IntroductionIn an issue of the American Mathematical Monthly [1] the following problemwas raised:"Determine all homeomorphisms f from [0,1] onto [0,1] that are solutionsof the functional equationf(Zx -- f(x)) = x for all x E [0,IJ.',Ratti and Lin [2] generalized the problem in two different directions. In thispapert we consider the following functional equationf(cr(x) df(x)) = F(x), (1.1)where c < 0,d > 0, c d = 1. We shall give the sufficient conditions ofthe existence, uniqueness a…