比较定理

Firstly, we prove the existence and uniqueness of the adapted solution of multi-dimensional backward stochastic differential equations driven by Brownian motion and Lévy process by using predictable representation theorem and the fixed point theorem about contract mapping, and also prove the comparison theory.

第一部分运用可料表示定理和压缩映射原理证明由布朗运动和Lévy过程共同驱动的多维倒向随机微分方程适应解的存在唯一性及其相应的比较定理。

Finally, we study the equivalence theorem and the comparison theorem of semiconvergence for the second quasi-nonnegative splitting.

最后讨论了第二型quasi非负分裂半收敛的等价定理和比较定理。

In part 1, we explore some properties of solution y of a backward stochastic differential equation, such as comparison theorem, reverse comparison theorem and uniqueness theorem of generator.

第一部分研究了倒向随机微分方程的解中y的性质，其中包括解的比较定理，逆比较定理，生成元的唯一性定理。

By using Lebesgue s dominated convergence theorem,several new comparison theorems for the oscillations of the difference equations with continuous arguments were established.

利用Lebesgue控制收敛定理，建立了具连续变量差分方程振动性的几个新的比较定理，给出了具连续变量差分方程强迫振动性的充分条件，并举例说明了强迫项对方程解的振动性的影响

In this paper, the authors consider the even-order neutral difference equations with continuous arguments. By using Lebesgue' dominated convergence theorem, a necessary and sufficient condition for the existence of eventually positive and bounded solutions is obtained.

研究一类具连续变量偶数阶中立型时滞差分方程，利用Lebesgue控制收敛定理给出这类方程存在最终有界正解的一个充分必要条件，得到相应新的比较定理。

Based on the fundamental theory of impulsive differential systems, employing Green formula, Gauss divergence theorem, Jensen inequality and Gronwall-Bellman inequality with impulse, we discuss the oscillation of impulsive partial differential systems by adopting reduction to absurdity and the stability in via of comparison theorem, respectively. Especially, we take an in-depth study on the oscillation of neutral impulsive parabolic systems and the stability of a class of nonlinear impulsive partial differential equations and obtain some useful conclusions.

本学位论文以脉冲微分系统基本理论为基础，利用反证法的分析方法和比较定理，结合Green公式、Gauss散度定理、Jensen不等式、含脉冲的Gronwall-Bellman不等式以及相关数学工具研究了脉冲偏微分系统的振动理论和稳定性理论，特别对中立型脉冲时滞抛物系统的振动性和一类非线性脉冲偏微分系统的稳定性作了较为深入的研究，给出了一些有用的结论。

On the base that two comparison theorems are established,applying the fixed-point theorems,we investigate the existence of maximal and minimal solutions forfirst order initial value problem and the JKjperiodic boundary value problem of discontinuous differential-integral equations of mixed type in partial-ordered Banach spaces,respectively.

在建立了两个比较定理的基础上，我们应用不动点定理，分别研究了半序Banach空间中不连续的一阶混合型微分-积分方程的初值问题与周期边值问题最大解与最小解的存在性。

This paper study the character and application of the solution of BSDE, the main results include: for the second kind of BSDE, the existence and uniqueness of the solution under non-Lipschitz condition, comparison theorem and stability are established , under weaker condition , the existence of the minimal and maximal solution is proved and the application in stochastic control and utility function is given; for the first kind of BSDE, under weaker condition , the existence of minimal and maximal solution .stability, comparison theorem and application to utility function are proved.

本文研究倒向随机微分方程解的性质及其应用，主要结果有：针对第二类方程，讨论了在非Lipschitz条件下倒向随机微分方程解的存在唯一性，比较定理及稳定性等，在更弱条件下，得到了倒向随机微分方程的最大解和最小解的存在性，在此基础之上，给出了在随机控制及效用函数方面的应用；针对第一类方程，同样在较弱条件下，证明了方程最大、最小解的存在性、稳定性、比较定理及其在效用函数的应用。

This paper study the character and application of the solution of BSDE, the main results include: for the second kind of BSDE, the existence and uniqueness of the solution under non-Lipschitz condition, comparison theorem and stability are established , under weaker condition , the existence of the minimal and maximal solution is proved and the application in stochastic control and utility function is given; for the first kind of BSDE, under weaker condition , the existence of minimal and maximal solution .stability, comparison theorem and application to utilityfunction are proved.

本文研究倒向随机微分方程解的性质及其应用，主要结果有：针对第二类方程，讨论了在非Lipschitz条件下倒向随机微分方程解的存在唯一性，比较定理及稳定性等，在更弱条件下，得到了倒向随机微分方程的最大解和最小解的存在性，在此基础之上，给出了在随机控制及效用函数方面的应用；针对第一类方程，同样在较弱条件下，证明了方程最大、最小解的存在性、稳定性、比较定理及其在效用函数的应用。

Through studying the singular points of the plane differential systems, the sufficient conditions of the nonexistence of limit cycle for the system are obtained by means of comparing theorem, analyzing divergence and change of variable.

通过对微分系统的奇点进行研究，借助比较定理，将该方程与其对称的方程进行比较，并通过分析散度和变量代换的定性分析，得到了其极限环不存在的充分条件。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。