一类二阶非线性差分方程的振动性与渐近性

研究了一类二阶非线性差分方程解的振动性与渐近性,建立了三个新的振动性与渐近性定理,推广和改进了已知的一些结果.     

一类三阶有理差分方程的奇点集和解的渐近性

研究三阶有理差分方程x_(n+1)=ax_(n-1)+x_(n-1)x_n/bx_(n-2)+cx_n,n=0,1,2,...的奇点集和解{x_n}_(n=-2)~∞的渐近性,其中a,b,c∈R,初始值x_(-2),x_(-1),x_0∈R.由a,b,c的取值的不同,而得到解的不同的渐近性.     

Asymptotic Solution of a Model Non-linear Convective Diffusion Equation

In this paper we consider the large-time solution of the equation for initial data with compact support. With m = 4 and n = 3the equation models the flow of a thin viscous sheet on an inclinedbed while for n m > 1 it has application in porous mediaflow under gravity. The equation can also be regarded as ananalogue of Burgers equation in non-linear diffusion. It isknown that two moving boundaries exist along which certain boundaryconditions are required to hold. The paper extends earlier workand determines the analytic behaviour of the moving boundariesexist along which certain boundary conditions are required tohold. The paper extends earlier work and determines the analyticbehaviour of the moving boundaries together with the structureof the solution which at large times is shown to depend cruciallyon the location in (n, m) parameter space.     

关于一类五阶常微分方程解的渐近性质

给出了一类五阶常微分方程所有解一致有界和当t→∞时收敛于零的充分条件。得到的结果包含并改善了Abou-El-Ela和Sadek1999年关于非自治微分方程渐近解的结果。     

On a Certain Difference Equation and Its Application to the Moment Problem

We study the difference equation $$\sum\limits_{m_1 ,m_2 } {\Omega [\sigma m_1 ,m_2 (z)] = g(z), z \in D,}$$ where D is the unit square, g(z) ∈ A(D), σ m₁, m₂(z) = z + m ₁ i + m ₂, |m ₁|+|m ₂| = 2, and Ω(z)∈ A(cD) is an unknown function.     

带强迫项的多时滞差分方程解的渐近性态

研究了一个带有强迫项的多时滞差分方程△x_n+sum from j=1 to m p_jx_(n-k_j)=r_n解的某种渐近性态.当这个方程的系数以及强迫项满足一定的约束条,其中p_j,r_n是实数,n,r_j是非负整数,λ_0是上述差分方程的特征方程的唯一实特征根,则表达式■λ_0~(-n)·x_n存在,并且给出了它的极限值.     

一类非线性时滞差分方程的渐近稳定性

本文考虑了时滞差分万程。x_n 1-x_n=-q_nx_(n-k(n)) G(n,x_(n-t(n)))零解的渐近稳定性，推广了文[2]的主要结果．     

Impossibility of a Certain Cyclotomic Equation with Applicationsto Difference Sets

Under certain conditions, we show the nonexistence ofan element in the p-th cyclotomicfield over , that satisfies . As applications, we establish the nonexistence ofsome difference sets and affine difference sets.     

一类二阶非线性中立型差分方程的振动性

研究了二阶非线性中立型差分方程Δ2(xn+pxn-l)+qnf(xn-k)=0的振动性,获得了该类方程振动的三个充分性定理.所得结果将一阶非线性中立型差分方程已有振动性的相应结论推广到了二阶非线性中立型差分方程.     

Asymptotic Behaviour of Trajectory Fitting Estimators for Certain Non-ergodic SDE

Suppose one observes a path of a stochastic processX = (X_t)_t≥0 driven by the equation dX_t=θ a(X_t)dt + dW_t, t≥0, θ ≥ 0 with a(x) = x or a(x) = |x|^α for some α ∈ [0,1) and given initial condition X ₀. If the true but unknown parameter θ₀ is positive then X is non-ergodic. It is shown that in this situation a trajectory fitting estimator for θ₀ is strongly consistent and has the same limiting distribution as the maximum likelihood estimator, but converges of minor order. This revised version was published online in August 2006 with corrections to the Cover Date.     

关于非线性狄立克雷问题的一致有效渐近解

本文研究最高阶导数项带小参数的二阶拟线性椭圆型方程的狄立克雷问题.在退化方程不存在奇点的情形下,当参数ε是充分小时,证明了解的存在性和唯一性,并在整个区域导出解的一致有效渐近近似式.     

Asymptotic Solution of a Non-linear Second Order Hyperbolic Differential Equation with Large Time Delay

The solution is given for a certain hyperbolic partial differentialequation with small non-linearity and large time delay includedinto both unperturbed and perturbed parts of the equation.     

The Asymptotic Behaviour and Blow-up Properties of Solutions of a Non-local Burgers' Equation

In this paper, we continue the work of [1] and obtain a complete picture of asymptotic behavior and blow-up properties of solutions of a non-local Burgers' equation.     

差分方程奇异摄动问题的渐近解

本文对含小参数的差分方程奇异摄动问题构造了一种新的渐近方法.     

On the Asymptotic Behaviour of General Partition Functions

For A = {a₁, a₂,...} N, let p_A(n) denote the number of partitions of n into a's and let q_A(n) denote the number of partitions of n into distinct a's. The asymptotic behaviour of the quotient is studied.     

On the Asymptotic Behaviour of Some Nonlocal Problems

The goal of this paper is to study diffusion problems associated with nonlinear diffusions of nonlocal type. We give existence and uniqueness results for these kind of problems and investigate the asymptotic behaviour.