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The variational convergence of real function sequence is extended to vector function sequence and the lower semicontinuity of approximating set of weak Pareto solutions of a given multiobjective decision making problem with general constraint set is obtained by using the variational convergence.

本文将函数序列的v－收敛性推广到向量值函数，在v－收敛性的条件下得到了给定的多目标决策问题的近似弱有效解集的下半连续性并给出了若干容易验证的充分条件。

At first, the existence of extended form of approach to continuous selection for any set valued mapping without any continuity restriction in para-compact metric space is proved ;by the topologically separated mappings , the approximate selection theorem of sub-lower-semi-continuous mapping is established, furthermore , continuous selection problem in H-space is studied. Next, with W-correspondence, an improved variational inequality is obtained ; by the H-KKM mapping ,Ky Fan\'s minimax inequality is generalized to H-space . At last, with H-convexity instead of the linear topological structure, a new version of Browder fixed point theorem is established.Chapter 3 deals with set-valued mapping vector variational inequality and minimax problems.

第二章首先在仿紧的度量空间上对任意的集值映射建立了新的逼近连续选择定理，利用映射的拓扑可分性，在H-空间上建立了次下半连续映射的逼近连续选择定理和一个新的连续选择定理；然后利用W-对应，在H-空间上建立了广义的变分不等式；利用H-KKM映射，在H-空间上建立了广义的KyFan极小极大不等式；最后，利用H-凸性代替拓扑线性结构，在H-空间上建立了一个新型的Browder不动点定理。

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。

Firstly, the three-dimension boundary question and its corresponding variation question concerning the point-source electrical field on a 3-D structure are presented. Secondly, the finite element method is used to solve the variational equation. The study area is divided into many tetrahedral elements. Then, we interpolate with a tri-linear function in each element. So, the variational equation is converted into a linear equation system. Finally, taking into account saving of time, we make use of symmetric successive overrelaxation preconditioned conjugate gradient algorithm to solve large linear system, and obtain the potential value of each node, resulting in the calculation of the apparent resistivity values on the ground surface.

首先给出了三维构造中点源电场的边值问题以及相应的变分问题；然后利用有限单元法求解变分问题，采用四面体单元对研究区域进行剖分，在单元中进行三线性函数插值，将变分方程化为线性代数方程组；最后，考虑到节约计算时间，利用对称超松弛预条件共轭梯度迭代算法求解大型线性方程组，得到了各节点的电位值，进而计算出地表的视电阻率。

The necessarity and sufficiency condition of weakly sequential semicontinuity for variational integrals are obtained in the setting of Orlicz-Sobolev space, which generalizes the corresponding results for variational problems with polynomial growth.

研究了非多项式增长的变分泛函，利用Orlicz空间理论，得到了其在Orlicz-Sobolev空间中弱序列下半连续的充要条件，推广了关于多项式增长的变分泛函的相应结论。

In this paper,we introduce the concepts of efficient solution for vector variational inequalities and f-quasimonotone operator,and give an existence theorem for vector variational inequalities in Banach spases.

引进了向量变分不等式有效解以及f－拟单调算子的概念，并给出了Banach空间中拟单调向量变分不等式的有效解的存在性定理

One of the most important extension is system of variational inequalities. In Chapter 5, we consider a system of generalized variational-like inequalities problems.

近年来，变分不等式已经开始向各个方向推广，出现了诸如广义变分不等式，混合变分不等式，广义似变分不等式等。

In this paper, some characterizations of solutions for a system of vector variational inequalities are derived under the assumption of PPM (where F and-F are both pseudomonotone). Moreover, a gap function for this system of vector variational inequalities is suggested and proved to be weak sharp minima under strong monotonicity.

该文研究了一类向量变分不等式组，在PPM条件下，对其解进行了一些刻画此外，给出了该向量变分不等式组的一个间隙函数，并在强单调条件下，证明了它是弱尖极小的。

Without considering the EM effect and using the generalized variational structure principle, It can get the corresponding variational structure equation.

通过用四面体单元和三棱柱单元对大地模型进行剖分、插值、总体集成，最后解方程，实现了在水平地形和起伏地形条件下频率域激电参数的正演模拟。2。

This integral equation is incorporated into a velocity-pressure variational formulation for the interior region, and a finite element method is used to approximate the resulting variational problem.

本文在绪论中简单介绍了边界元的发展历史及其发展现状，并把边界元和有限元做了简单的比较，介绍了它们各自的优缺点。

Now she was hungry and angry.She began to smoulder.

现在她又饿又气，她开始流露难以抑制的怒火。

You have placed our iniquities before You, Our secret sins in the light of Your presence.

诗90：8 你将我们的罪孽摆在你面前、将我们的隐恶摆在你面光之中。