The Similarity Method for Difference Equations

In this paper, the similarity method is applied to ordinarydifference equations. When a system of difference equationsadmits symmetries, it follows that the order of equations canbe reduced. Here, by a symmetry is meant a continuous groupwhich leaves the equations invariant. In particular, when aone-dimensional difference equation admits a symmetry, the equationbecomes a linear one and an analytic expression for the solutionmay be obtained. Two examples are given in the final section.     

Difference Equation for Functions Analytic Outside Two Squares

We consider a totality of two squares built on primitive periods 1 and i and “sufficiently close to each other“. In a vicinity of this set we investigate four-element difference equation with constant coefficients, whose linear shifts are generating transforms of the corresponding doubly periodic group and the inverse transforms. We seek a solution in a class of functions, which are analytic outside this set and vanish at infinity. The equation is applicable to the moments problem for entire functions of exponential type.     

带有多个变滞量的二阶中立型差分方程振动性判据

研究了一类较广泛的带有多个变滞量的变系数的二阶中立型差分方程的振动性 ,给出了该类方程振动及差分算子△振动的判据 .     

一类二阶中立型微分差分方程周期解的存在性

考虑如下二阶中立型微分差分方程的边值问题：{x(t-τ)-x(t-τ） f(t,x(t),x(t-τ）,x(t-2τ）=0 x(0)=x(2kτ），x（0）=x（2kτ）其中k是任意给定的正整数,τ 为正实数，利用含有偏差变元的变分结构及临界点理论，作给出了判定上述方程存在非平凡周期解的判定准则。     

一类非线性时滞差分方程解的若干性质

本文研究了一类非线性时滞差分方程解的有界持久性、全局渐近稳定性以及无界解的存在性,所得结果解决及部分解决了文献「４」提出的两个ｏｐｅｎ问题,包含了文献「６」中相应的结果。     

A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations

<正>We consider a finite difference scheme for a nonlinear wave equation,whose solutions may lose their smoothness in finite time,i.e.,blow up in finite time.In order to numerically reproduce blow-up solutions,we propose a rule for a time-stepping, which is a variant of what was successfully used in the case of nonlinear parabolic equations.A numerical blow-up time is defined and is proved to converge,under a certain hypothesis,to the real blow-up time as the grid size tends to zero.     

非线性时滞差分方程周期解的存在性

主要研究一阶非线性时滞差分方程△x（n）=-f（x（n-T））的非平凡周期解的存在性与多解性．应用临界点理论,在,满足一定的增长性条件下,得到了上述方程存在非平凡周期解的一系列充分条件．另外,还通过若干例子阐明结论的可行性。     

New Explicit and Exact Solutions for the Klein-Gordon-Zakharov Equations

In this paper, based on the generalized Jacobi elliptic function expansion method, we obtain abundant new explicit and exact solutions of the Klein-Gordon- Zakharov equations, which degenerate to solitary wave solutions and triangle function solutions in the limit cases, showing that this new method is more powerful to seek exact solutions of nonlinear partial differential equations in mathematical physics.     

常系数线性差分方程的微分解法

用微分方法 ,解常系数线性差分方程     

一阶中立型差分方程非振动解的分类

讨论了中立型差分方程的非振动解.首先由非振动解的渐进性质把非振动解分成两类.其次分别给出存在这两类非振动解的充分条件.最后给出例子说明定理的应用.     

具多滞量的非线性中立型差分方程的振动性定理

研究了一类较为广泛的具有多个滞量的非线性中立型差分方程的振动性,得到了该类方程振动的一个判定定理     

Sufficient Conditions for the Oscillation of Non-autonomous Difference Equations

Abstract In this paper, we obtain sufficient conditions for the oscillation of the non-autonomous differenceequations x(n 1)-x(n) sum from i=1 to m p_i(n)x(n-r_i(n))=0,which are the discrete analog of the delay differential equations considered in[1].     

电报方程双周期解的极大值原理与强正性估计及应用

本文讨论非线性电报方程u_(tt)-u_(xx)+cu_t=F(t,x,u),(t,x)∈R~2时空双2π周期解的存在性。改进了Ortega与Robles-Perez关于线性电报方程双周期解的极大值原理,应用新获得的极大值原理,推广了相应的上下解定理,并且加强了极大值原理的结论,建立了线性方程解的强正性估计,利用这个强正性估计及锥上的不动点定理获得了超线性电报方程及奇异电报方程正双周期解的存在性。     

Logistic差分方程单个和多重周期正解的存在性

研究了Logistic差分方程单个和多重周期正解的存在性理论,利用锥不动点定理证明了解的存在性,并应用本文的理论验证了一些生物数学模型.     

具有连续变量的多时滞二阶中立型差分方程的振动准则

本文用分析的方法研究了一类具有连续变量的多时滞二阶中立型差分方程解的振动性，给出了该类方程解振动和差分算子振动的几个充分条件．     

Kamenev Type Oscillation Criteria for Nonlinear Difference Equations

By means of Riccati transformation techniques, we establish some new oscillation criteria for second-order nonlinear difference equation which are sharp.     

二阶半线性中立型差分方程的振动性准则

考虑二阶半线性中立型差分方程给出了方程(1)的解的振动性的充分条件．所有结果推广和改进了关于中立和时滞差分方程已有结果．     

非线性时滞差分方程的线性化振动性

本文分临界和非临界两种情形，建立了非线性时滞差分方程与其线性化方程振动性等价定理，推广和改进已有的工作．作为推论，修正了文[２］中主要定理的错误．     

一阶中立型时滞差分方程振动的充分必要条件

研究了一阶常系数中立型时滞差分方程A[x(n)-px(n-τ)]+qx(n-σ)=0的振动性.通过构造若干适当的函数,分别得到了在01两种情况下该方程的一切解振动的充分必要条件.