JULIA LIMITING DIRECTIONS OF ENTIRE SOLUTIONS OF COMPLEX DIFFERENTIAL EQUATIONS

For entire or meromorphic function f,a value θ ∈[0,2π) is called a Julia limiting direction if there is an unbounded sequence {zn} in the Julia set satisfying l...     

线性微分方程亚纯解的Julia集的径向分布

本文研究了线性微分方程f(n)+An-1f(n-1)+···+A1f+A0f=0亚纯解的动力学性质,其中n≥2,Ai(z)(i=0,1,···,n-1)是具有有限下级的亚纯函数.利用亚纯函数的Nevanlinna值分布理论,获得了一定条件下方程亚纯解的Julia集的径向分布的下界,推广了相关文献的结果.     

STABILITY OF SOLUTIONS TO CERTAIN FOURTH-ORDER DELAY DIFFERENTIAL EQUATIONS

By the Lyapunov functional approach, some better results on the asymptotic stabiBy the Lyapunov functional approach, some better results on the asymptotic stability and global asymptotic stability of zero solution to a certain fourth-order non-linear differential equation with delay are obtained.     

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。     

STABILITY OF THE SOLUTIONS TO STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this paper,we obtain the stability of solutions to stochastic functional differential equations with infinite delay at phase space BC((-∞,0];Rd),under non-Lipschitz condition with Lipschitz condition being considered as a special case and a weakened linear growth condition by means of the corollary of Bihari inequality.     

ON THE EXISTENCE OF ALMOST PERIODIC SOLUTIONS OF SOME DELAY DIFFERENTIAL EQUATIONS

By means of exponential dichotomy, this paper investigates the existence of almost periodic solutions of some delay differential equations.     

一类高阶整函数系数线性微分方程解的超级

本文利用值分布理论,对高阶整函数系数线性微分方程(其中存在两个系数的级相等且最大)的解的复振荡性质进行了研究,得到了方程解的超级的精确估计.     

费马q-差分微分方程整函数解的增长性研究

本文研究了费马q-差分微分方程的整函数解的相关问题.利用经典和差分的Nevanlinna理论和函数方程理论的研究方法,获得了q-差分微分方程整函数解增长性的几个结果.     

SPURIOUS NUMERICAL SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS

This paper deals with the relationship between asymptotic behavior of the numericalsolution and that of the true solution itself for fixed step-sizes. The numerical solution isviewed as a dynamical system in which the step-size acts as a parameter. We present aunified approach to look for bifurcations from the steady solutions into spurious solutionsas step-size varies.     

ON ALGEBRAIC SOLUTIONS OF THE SECOND-ORDER COMPLEX DIFFERENTIAL EQUATIONS WITH ENTIRE ALGEBRAIC ELEMENT COEFFICIENTS

The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coefficients.Several theorems on the existence of solutions are obtained,which perfect the solution theory of linear complex differential equations.     

具有时滞的双曲型微分方程解的振动性

在本文中，我们研究具有时滞的双曲型微分方程解的振动性其中是具有逐片光滑边界的有界区域，得到了方程（１）的解振动的若干充分条件．     

一类整函数系数线性微分方程解的增长级和零点

在本文中假设微分方程的系数为有限级整函数且满足：对于每个不恒等于零的系数Aj(j为整数且0≤j≤k-1)，其零点收敛指数小于其增长级，且当Ai≠0,Aj≠0(i≠j),Ai/Aj的增长级等于Ai与Aj增长级的最大值，以及自由项F为有限级整函数。我们研究了线性微分方程f^(k) Ak-1f(^k-1) … A0f=f,k≥2解的增长级和零点收敛指数，得到在一定条件下，方程解的增长级及零点收敛指数的精确估计。     

ENTIRE SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENTS HAVING THE SAME ORDER

In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.     

数值求解比例延迟微分方程的收敛性

本文主要讨论p阶CRK方法数值求解比例延迟微分方程 :U′(t) =f(t,U(t) ,U(qt) ) ,U(0 ) =U0　0 ≤t≤H0 相似文献   

ON THE STABILITY OF SOLUTIONS TO A CERTAIN FOURTH-ORDER VECTOR DELAY DIFFERENTIAL EQUATION

In this paper, by constructing a Lyapunov functional, sufficient conditions for the uniform stability of the zero solution to a fourth-order vector delay differential equation are given.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A CLASS OF SECOND ORDER QUASILINEAR DIFFERENTIAL EQUATIONS WITH DELAY DEPENDING ON THE UNKNOWN FUNCTION

The asymptotic behavior of the solutions to a class of second order quasilinear differential equations is considered. The main results improve and generalize those in Elbert and Kusano [3].     

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO NONLINEAR DELAY FRACTIONAL DIFFERENTIAL EQUATIONS

Using a fixed point theorem,this paper discusses the existence and uniqueness of positive solutions to a system of nonlinear delay fractional differential equations and obtains some new results.     

POSITIVE SOLUTIONS TO TWO TYPES OF NEUTRAL DIFFERENTIAL EQUATIONS WITH DISTRIBUTED DELAY

In this paper, we study two types of neutral functional differential equations with finite or unbounded distributed deviating arguments. By Banach contraction princi-ple, we obtain some sufficient conditions for the existence of positive solutions to such equations.     

EXISTENCE OF MILD SOLUTIONS TO NEUTRAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this paper, we consider the existence of mild solution to a class of neutral fractional differential equations with infinite delay. By means of fixed points methods, we obtain some sufficient conditions for the existence and uniqueness of mild solutions, which extend some known results.     

THE DISTRIBUTION OF ZEROS OF SOLUTIONS OF NEUTRAL DIFFERENTIAL EQUATIONS WITH A VARIABLE DELAY

In this paper, the distribution of zeros of solutions of the first-order neutral differential equation with a variable delayis studied. The estimate for the distance between adjacent zeros of the oscillatory solution of the above equation is obtained.