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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。

Two-point boundary value problems of second order mixed type integro-differential-difference equation is studied by means of differential inequality theories.

利用微分不等式技巧研究了某一类二阶混合型积分微分差分方程的两点边值问题,在上下解存在的条件下,得到了解的存在性和唯一性定理。

In 2000,Zhou Wenshu gained the existence and uniqueness of the strict convex classical solutions of the third initial-boundary value problems of the Monge - Ampere.

2000年,周文书[10]得到了如下形式的抛物型Monge-Ampère方程的第三初边值问题严格凸古典解的存在唯一性本文的目的是把[10]的结果进行一般性的推广,考虑下列非线性抛物型Hessian方程的第三初边值问题抛物型H。

In part 3, utilizing the existing Lipschitz results and the property of Yosida approximation of monotone and continuous function, we prove the existence and uniqueness theorem of a general backward stochastic differential equation with monotone and continuous coefficient.

第三部分在系数仅满足单调连续这样一个新条件下,我们综合运用单调连续函数的Yosida逼近的性质以及Lipschitz条件下的已有结果,证明了一般形式的倒向随机微分方程解的存在唯一性

By using the cone theory and the iterative technique, the existence and uniqueness of positive fixed point for a class noncompact mixed monotone operator are studied.

本文利用锥理论和迭代技巧,研究了一类非紧混合单调算子正不动点的存在唯一性,改进和推广了混合单调算子、增算子与减算子的某些相应结果。

As an appliance, by applying the addition defined in this paper, the uniqueness theorem of meromorphic functions obtained by Yang Lo is generalized which consider its multiple values to multiple valued algebroidal functions.

本文明确地定义了加、乘运算,并证明了运算后的结果仍是代数体函数。为进一步的研究完善了理论基础。关于亚纯函数的唯一性定理有许多非常好的成果仁'1。杨乐创造了一种方法,结合重值更深人的研究了亚纯函数的值分布〔,一'了。

Using Nevanlinna value distribution theory, the research we studies the uniqueness of meromorphic functions concerning the multipliable value, and proves one theorem, which generalizes and improves previous results.

运用亚纯函数的值分布理论,研究了亚纯函数涉及重值的唯一性问题,证明了一个定理,所得定理改进了先前的一些结果。

Then several structural theorems of regular power rings and uniform power rings are established respectively and the uniqueness of the multiplication of a regular power ring is proved.

建立了正则幂环与一致幂环的结构定理,并证明了正则幂环的乘法运算的唯一性

In the third chapter, we study the existence, uniqueness, global stability of positive solution and MLEs of parameters of Lotka-Volterra competition system, mutualism system and predator-prey system with random perturbation.

第三章研究了具有随机扰动的Lotka-Volterra型的竞争系统,互惠系统和捕食-被捕食系统正解的的存在性,唯一性,全局渐近稳定性以及参数的极大似然估计。

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