定理

In the present paper, some theorems for variational inequalities and minimax inequality are obtained in hyperconvex metric space s.

摘要文章给出了超凸度量空间中的一些变分不等式定理和极大极小不等式定理。

The first systematic and fundamental research is did by Modigliani and Miler, they bring out with the famous MM theorem in 1958.Which says capital structure doesn't affect enterprise market value and average capital cost in a condition of perfect market. After that, several economists including Modigliani and Miler themselves put this theory forward with the MM theorem with the consideration of tax, the trade-off theory, the pecking order theory,market for corporate control, these analyses throw lights on the problem from different aspect.

对此做出系统性和开创性研究的是Modigliani和Miler，在1958年提出了资本成本与资本结构无关的MM定理，在此基础上，包括Modigliani和Miller在内的许多经济学家对此进行了探索，他们先后提出了考虑税收的MM定理、权衡理论、优序融资理论、控制权理论，从不同的角度分析了资本结构的优化问题。

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。

In the present paper, some theorems for variational inequalities and minimax inequality are obtained in hyperconvex metric spaces.

文章给出了超凸度量空间中的一些变分不等式定理和极大极小不等式定理。

Equilibrium; continuous selection; the fixed point theorem; variational inequality; minimax theorem; H-space

基础科学，数学，数学分析均衡；连续选择；不动点定理；变分不等式；极小极大定理； H-空间

A complete novel assumption is presented. Then, we prove the existence of two nontrivial solutions for a class of second order superlinear difference systems with the help of Minimax principle and Linking theorem in critical point theory,.6. Two applications in physics are given. Firstly, a coupled differential system coming from second harmonic waves is discussed.

利用Ricceri建立的三临界点定理，证明了一类含参数二阶差分方程在某些新的条件下至少存在三个解；随后，利用临界点理论中的极小极大原理和环绕定理，讨论了一类二阶超线性差分方程组多重解的存在性。

The abstract result contains several concrete results in the literature and can also be used to deal with some new cases for resonant differential equations.In the introduction, we briefly introduce the development process of the variational methods. In Chapter 2, we list some basic knowledges refering to the variational methods, including the Sobobev space,—△ operator, the weak solution and the minimizing sequence methods and some minimax theorems. In Chapter 3, we introduce the research process of Hamiltonian system of second order and the semilinear elliptic problems, using the methods introduced previously. In Chapter 4, we prove the main theorem of the thesis, and apply it to the problems in the previous Chapter, and can also be applied to some new resonant cases.

在前言中，简要介绍了变分法的产生、发展过程，在第二章中我们介绍了有关变分法的一些基本知识，包括Sobolev空间，—△算子，弱解，极小化序列方法和一些极小极大定理，在第三章中我们介绍了非线性项有界或满足次线性条件，以及它满足推广的Ahmad-Lazer-Paul条件时，二阶Hamiltonian系统和半线性椭圆问题的研究历程，最后在第四章中我们证明了本论文的主要定理，并把它应用到第三章的问题中，使得前面的几种共振的情形都可以统一到这个抽象的结果中。

According to theorems of momentum and moment of momentum and helmholtzs equation, motion quations of the tethered system are obtained.

根据动量定理、动量矩定理和Helmholtz方程建立了系统动力学方程。

The general expression of the moment of momentum of particles relative to an arbitrary point is discussed including application of the theorem of the plane movement in rigid body .

讨论了质点系相对于任意点的动量矩定理的一般表达式及该定理在刚体平面运动中的应用。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐