THE COMPLEX OSCILLATION OF NON－HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS WITH INFINITE ORDER ENTIRE COEFFICIENTS

ＴＨＥＣＯＭＰＬＥＸＯＳＣＩＬＬＡＴＩＯＮＯＦＮＯＮ－ＨＯＭＯＧＥＮＥＯＵＳＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＩＮＦＩＮＩＴＥＯＲＤＥＲＥＮＴＩＲＥＣＯＥＦＦＩＣＩＥＮＴＳ￥ＬｉＸｉａｎｙｕ（李贤瑜）（ＪｉａｎｇｘｉＮｏｒ...     

关于高阶整函数系数微分方程解的超级

研究两种类型的高阶线性齐次整函数系数微分方程解的增长性问题。对于这两种类型的方程,当存在某个系数对方程的解的性质起主要支配作用时,得到了方程解的超级的估计,特别是对零点收敛指数是有穷的解,得到了解的超级的精确估计。     

求P阶整函数零点的一簇大范围收敛的迭代法

考虑下列方程: f(x)=0 (1)的求根问题。本文始终假定f(x)是只含实零点的p阶整函数,p是任一正整数。这里的f(x)在实用上是很广泛的一类函数。任给一实数x_0,假定对实数h>0,(1)在|x-x_0±h|≤h上无根;又设q是大于p的正整数,我们给出如下具有大范围收敛的一簇迭代公     

整函数的可计算性

若已知整函数f(z)在一个具有聚点z_0的无限集D上的值,则从理论上说,可由估计f(z)在z_0的各阶导数再对f(z)在该点展成幂级数来计算f在D以外点处的值.很明显,这种过程在实际计算中是不可取的.此时的可计算性,是指对任何z?D及ε>0,     

POSITIVE ENTIRE SOLUTIONS TO NON-LINEAR p-LAPLACE SYSTEMS

We consider the N-dimensional singular p-Laplace systems and obtain some sufficient conditions which guarantee that the system has infinitely many radial positive entire asymptotic solutions.     

超越整函数的某些动力学性质

本文研究了由m个超越整函数{fl,f2,…,fm}生成的随机迭代系统的Fatou集分支的某些动力学性质.运用复动力系统理论与双曲度量理论,得到了随机迭代系统有界Fatou分支不存在的一个判别准则,同时回答了Baker所提出的问题,且给出了随机迭代系统Fatou分支为单连通的一个充分条件,推广了Bergweiler的结果.     

ON ENTIRE FUNCTIONS, BLOCH AND NORMAL FUNCTIONS

New criteria for an analytic function to be Bloch and for a meromorphic function to benormal are given. These criteria generalize the recently introduced area integral conditionsinvolving a Green's function.     

极大外平面图的边面全色数

本文给出了△（Ｇ）≤６的极大外平面图的边面全色数，其中△（Ｇ）表示Ｇ的最大度。     

涉及导数与公共值的整函数

本文研究整函数f与f'具有一个公共值时的R.Brck问题,用一种较简便的方法证明了:若f与f'以有穷非零复数a为IM公共值,且存在正数M,使f(z)=a时0<│f'(z)│≤M,则f'a/f-a≡c,其中c为非零常数、此结论改进了G.Jank等人的结果。     

奇异半线性椭圆方程的非径向正整体解

研究如下N维奇异半线性椭圆方程△u+f(x,u)=0, x∈RN(N≥3),其中函数f:RN× R+→R+连续,在u=0有奇异性;采用上-下解方法给出该方程具有满足如下性质的有界正整体解u的条件: u∈C2+θloc(RN)使得lim |x|→∞ u(x)=0且u(x)≥εmin{1,|x|2-N},其中ε＞0是常数;并证明:若条件添加"f关于u单调不增"的限制,则这种解是唯一的.     

ENTIRE CHROMATIC NUMBER AND △-MATCHING OF OUTERPLANE GRAPHS

Let G be an outerplane graph with maximum degree A and the entire chromatic number Xvef（G）. This paper proves that if △ ≥6, then △＋ 1≤Xvef（G）≤△＋ 2, and Xvef （G） = △＋ 1 if and only if G has a matching M consisting of some inner edges which covers all its vertices of maximum degree.     

关于整函数及其微分多项式的唯一性

本文讨论关于整函数及其微分式项式的唯一性，所得定理推广文[1],[[2]的一些结论。     

ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL

This paper is mainly concerned with entire solutions of the following two-species Lotka-Volterra competition system with nonlocal(convolution) dispersals:■Here a ≠1,b≠1,d,and r are positive constants.By studying the eigenvalue problem of(0.1) linearized at(Φc(ξ),0),we construct a pair of super-and sub-solutions for(0.1),and then establish the existence of entire solutions originating from(Φc(ξ),0) as t→-∞,where Φc denotes the traveling wave solution of the nonlocal Fisher-KPP equation u_t     

半平面上无限级Dirichlet级数的上下级

本文研究了右半平面上无限级Dirichlet级数的增长性及正规增长性.利用熊庆来的型函数及Newton多边形,得到了Dirichlet级数的下级与其系数的关系.     

MINIMAL POSITIVE ENTIRE SOLUTION OF SEMILINEAR ELLIPTIC EQUATION

In this paper, the singular semilinear elliptic equation Δu+q(x)u^α+p(x)u^-β-h（x)u^γ=0,x∈R^N,N≥e,is studied via the super and sub-solution method, where Δ is the Laplacian operator, α∈[0,1),β&gt;0,and γ≥1 are constants. Under a set of suitable assumptions on functions q(x), p(x) and h(x), it is proved that there exists for the equation one and only one minimal positive entire solution.     

论一类整函数的牛顿级数展式

本文给出级小于1的整函数的牛顿级数展式的充要条件．     

整函数及其k阶导函数的唯一性

本文研究了整函数及其k阶导函数的唯一性问题．利用正规族理论．证明了整函数及k阶导出数是等价的．改进和推广了Mues，Steinmstz，李江涛以及仪洪勋等人的有关结果．     

THE PITS PROPERTY OF ENTIRE FUNCTIONS DEFINED BY DIRICHLET SERIES

The value distribution of entire functions defined by Dirichlet series are studied in this present article.It is proved that entire functions defined by Dirichlet series have the pits property,which improve the relative results on lacunary Taylor series obtained by Littlewood J.E.and Offord A.C.