对一类二阶非线性差分方程的解给出了几个振动或非振动的判定定理，并举例说明了定理的应用。
Some new criteria of oscillation or non-oscillation are presented for certain nonlinear second order difference equations. Several examples are given to illustrate the results.
研究了一类具有多个变滞量的变系数的二阶中立型差分方程的解的振动性，得到了该类方程振动及其解的一阶差分振动的充分条件。
The oscillation problem for a class of the second order neutral difference equations with several variable delay arguments and variable coefficients was studied.
研究了一类具有多个变滞量的变系数的二阶中立型差分方程的解的振动性，得到了该类方程振动及其解的一阶差分振动的充分条件。
The oscillation for a class of the second order neutral difference equations with several variable delay arguments and variable coefficients are studied.
对差分方程的研究就是讨论它的解的最终性态，包括振动性、循环长度及全局渐近稳定性等。
The investigation on difference equation is to discuss its eventually behavior of the solutions, including oscillation, cycle length and global asymptotic stability, etc.
通过构造差分方程的周期数列解，研究了一类具有分段常数变元的脉冲微分方程周期解的存在性。
The existence of periodic solutions for a class of impulsive differential equations with piecewise constant argument is studied by constructing periodic sequence solutions of difference equation.
摘要通过对积分算子谱的估计，作者给出了一阶线性微分差分方程在边值条件下解的存在唯一性定理。
In this paper, by estimates of spectral of an integral operator, the authors give a theorem on the existence of solutions for first order differential difference equations with boundary condition.
主要的方法是利用矩阵差分方程的特征矩阵方程解的性质。
The main method is using the properties of the solutions of characteristic matrix equation.
利用拓扑度理论对一类非线性泛函差分方程周期解的存在性进行了讨论，得到该问题周期解的一个存在定理。
The existence of periodic solution to nonlinear functional difference equation is considered by using the topological degree, and a periodic solution of this problem is obtained.
这是首次研究差分方程的双向渐近解的存在性并获得了满意的研究成果。
This is the first time to discuss homoclinic solutions for difference equations, some satisfactory results are obtained.
用交错网格的高阶有限差分方法解波动方程，在满足稳定性要求时，可获得时间和空间都是高阶精度的结果。
Highly precise solutions both in time and in space can be reached by solving wave equation with high order finite difference scheme of staggered grid under the condition of stability.
进一步地，我们采用二分法与相平面分析结合的方法计算压差方程的数值解。
Furthermore, we compute the Riemann solution by using a bisection method combined with the phase-plane analysis.
本文主要讨论了差分方程的概周期解与伪概周期解的存在性。
In this paper, we investigate the existence of almost periodic solutions and pseudo almost periodic solutions for difference equations.
利用两种不同的网格精细化方法与差分方程解的外推过程相结合，能更精确地求解等离子体平衡方程。
We adopt two kinds of different mesh refinement process combining extrapolation of difference solution for more accurately solving tokamak plasma equilibrium equation.
应用现代差分方程理论对这些数学模型解的渐近性态与周期振荡进行了详细的讨论研究。
The asymptotical behaviors and periodic oscillations have been studied by applying the modern theories of difference equations.
适用于MATLAB的数值方法用来解动力分析采用的差分方程。
Numerical methods available in MATLAB for solving the ordinary differential equations are employed for the dynamic analysis.
差分方法是解偏微分方程的有效而实用的方法，它的计算量小，精确度高。
The difference method is efficient and practical method to solve the partial differential equation, which has some advantages of a little computational effort and high accuracy.
利用不动点方法及对差分方程构造概周期解，获得了概周期解存在的充分条件。
By using fixed point theorem and constructing almost periodic sequence solution for difference equation, the authors get the sufficient conditions for the existence of the almost periodic solution.
该文讨论了一类二阶非线性中立型差分方程解的振动性，扩充并改进了此类方程的已有结果。
The autheors obtain results on the oscillations of solutions of a second order nonlinear neutral difference equation.
本文讨论常微分方程差分周期解的几何性质。
In this paper the geometric properties of the difference periodic solutions of ordinary differential equations are discussed.
通过对积分算子谱的估计，作者给出了一阶线性微分差分方程在边值条件下解的存在唯一性定理。
In this paper, by estimates of spectral of an integral operator, the authors give a theorem on the existence of solutions for first order differential difference equations with boundary condition.
第三章利用矩阵理论与重合度理论，讨论了一类非自共轭非线性二阶差分方程周期解的存在性问题。
Chapter 3 is centered around the existence of periodical solutions for non self-adjoint nonlinear second order difference equations by invoking matrix theory and coincide degree theory.
差分方程研究的主要内容包括两个问题：差分方程的精确解和方程解的定性分析。
The study of difference equations is main about two problems: exact solutions of the equations and qualitative analysis of the solutions.
研究了三阶Poincaré差分方程解的渐近性质。这种差分方程对应的常系数线性差分方程的特征方程有重根。
We studied the asymptotic behavior of solutions to third order Poincaré difference equation whose characteristic equation has multiple roots.
研究了三阶Poincaré差分方程解的渐近性质。这种差分方程对应的常系数线性差分方程的特征方程有重根。
We studied the asymptotic behavior of solutions to third order Poincaré difference equation whose characteristic equation has multiple roots.
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