theory of differential equations

Two Results on the Complex Oscillation Theory of Differential Equations with Polynomial Coefficients

关于多项式系数微分方程复振荡理论的两个结果

Application of the quantitative theory of ordinary differential equations to analyzing a dynamic crack tip-field

常微分方程定性理论在动态裂纹尖端场分析中的应用

In the first one, we introduce the history of the qualitative and bifurcation theory of differential equations, some present results and our main work.

第一部分文献综述，介绍了分支理论的发展历史及其现状，并简要叙述了本文的主要工作。

The theory of the solution of partial differential equations remained to be fashioned.

偏微分方程解的理论还有待于形成.

The Application of Fourier Method to the Theory of Partial Differential Equations

Fourier方法在偏微分方程理论中的应用

In the part of introduction in the first chapter, we introduce the development of oscillation theory of ordinary differential equations and functional differential equations briefly.

在第一章绪论部分，一方面我们简单介绍了常微分方程振动理论与泛函微分方程振动理论的起源与发展。

Exact response of damped linear vibrating systems to arbitrarily excitation is obtained according to theory of ordinary differential equations.

利用常微分方程组理论在较一般条件下求出了线性有阻尼多自由度振动系统对任意外激励的精确响应。

This paper deduces a water quality model by using the theory of random differential equations, and proposes a stochastic method for water quality management at a river.

运用随机微分方程理论，推导了一个水质模型，提出了河流水质管理的随机规划方法。

In the study of the qualitative theory of differential equations, especially in the study of the stability of differential equations, the estimate of solutions and the boundedness of solutions, Gronwall-Bellman-Bihari inequality can be used as handy tools.

在探讨微分方程定性理论中，尤其在探讨微分方程（组）的稳定性、解的估计及有界性的过程中，Gronwall-Bellman-Bihari不等式是一强有力的工具。

The Properties and Applications of the Integrating Factor in the Qualitative Theory of Ordinary Differential Equations

积分因子在定性理论中的性质及其应用

In the waveguide problems of this paper, results obtained cannot be directly found in the existing literature and have been worked out from fundamental theory of differential equations.

在本文所讨论的波导问题中，所得结果不能直接从现有文献中导出。我们已经从基本微分方程理论中算出了这些结果。

Based on the theory of differential equations, the authors assume that energy flows on first and second order processes, then establish and analyse the compartment model.

以微分方程理论为基础，假设能量按一级和二级动力学过程流动，建立了生态网络中的能量流动分室模型并进行了分析。

Firstly sufficient conditions for the existence of periodic solution are obtained by comparison theory of reaction-diffusion differential equations;

利用反应扩散方程的比较原理给出了系统存在周期解的充分条件。

A model of evolutionary game is designed and the EES solutions of the model are obtained by using the theory of differential equations. Based on the analysis we put forward the incentives mechanism for enterprises joining a cluster. 3.

使用微分方程稳定性理论求出了该博弈模型的稳定均衡解，并画出演化博弈的相图进行分析，在分析的基础上提出了企业入群的激励机制。

The singular boundary problems of nonlinear differential equations are important subjects in the theory of differential equations.

非线性微分方程奇异边值问题是微分方程理论中的一个重要课题。

The method used is the theory of partial differential equations.

本文内容为数字图像复原技术的研究，采用的方法为偏微分方程理论。

Theory of Functional Differential Equations with Random Impulse

随机脉冲泛函微分方程理论

Boundary value problems ( BVPs) of functional differential equations ( FDEs) arise frequently in application of optimal control theory and circuit theory.

泛函微分方程边值问题广泛出现在最优控制理论及电路理论的应用之中。

Aiming at the solving problem of equilibrium solution of this nonlinear model, geometry theory of differential equations is adopted, and the relative calculation formula is given.

采用微分方程几何理论分析河流综合水质模型的基本方程，探讨了河流综合水质模型的平衡状态解的求解方法，并给出相关计算公式。

The generalized kink waves of the short pulse equation were studied by the qualitative theory of ordinary differential equations and numerical simulation method.

用微分方程定性理论结合数值模拟方法研究了窄脉冲方程的广义扭结波。

In the theory of impulsive differential equations, we call the discontinuous trajectories as impulses.

在脉冲动力系统理论中，把这种瞬时突变的现象称之为脉冲。

On the other hand, Lyapunov second method plays an important role in the establishment and development of stability theory of differential equations.

Lyapunov第二方法则对微分方程的稳定性理论的建立和发展起到了重要的作用。

Besides, we design and implement the image filtering algorithm based on the theory of partially differential equations to avoid the noise during enhancement.

最后针对图像增强中的噪声问题，设计实现了基于偏微分方程的图像滤波算法。

The global asymptotic stability of the positive equilibrium of the model with one population is considered by using the monotone theory of functional differential equations.

首先利用泛函微分方程的单调理论分析了单种群chemostat模型正平衡点的全局渐近稳定性。

First, we present numerical stability theory of delay differential equations and parallel methods.

首先, 我们介绍了延迟微分方程数值解的稳定性理论及并行算法的发展情况.

Numerical Solutions of a Gas Concentration Field Based on the Superposition Theory of Partial Differential Equations

基于叠加原理的气体浓度场数值计算方法

Based on the stability theory of stochastic differential equations, the sufficient conditions ensuring the successful consensus are given.

利用随机微分方程的稳定性理论，给出了多智能体系统达到一致性的充分条件。

In this paper, by using the theory of differential equations, we discuss the propagation regularity of computer viruses, especially the virus propagation model for the latent period.

本文利用微分动力系统理论研究了计算机单种病毒的传播规律，特别是研究了考虑计算机病毒潜伏期的病毒传播模型。

The oscillation theory of functional differential equations has a rapid development in the recent 30 years, see [ 1-4].

泛函微分方程的振动理论作为泛函微分方程定性理论的一部分，在最近30多年中有了迅速的发展，见[1-4]。

The generalization is quite similar to the corresponding one in the theory of differential equations.

这一推广和对应的微分方程中理论的推广相当类似.