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The aim of this paper is to study the existence of solution and multiply results for quasilinear elliptic system in bounded domain and the whole space, semilinear elliptic equation in two dimension space, second order nonlinear difference equation by variational methods. The main results are listed in the following:1. An abstract compactness theorem is proved, and then, under weak Boccardo and De.

本文主要利用变分法，分别研究了有界区域和全空间上拟线性椭圆型方程组、二维空间上半线性椭圆型方程和二阶非线性差分方程问题的解与多重解的存在性，具体内容如下： 1。

The author proves theorem on contracting maps for halfmetric space and the existance of solution and the Continuousness of integral operator integral equation in Orlica space.

证明了半度量空间中的压缩映像原理，并应用其证明了Orlica空间中一类积分方程解的存在性及积分算子的连续性。

The coordinate transformation and numerical integration was executed on the discretized tetrahedral elements based on which the 3-D MT vector-finite element method was implemented. A whole computation framework for 3-D vector-finite element method with unstructured mesh was given. Based on this some typical models were tested which has demonstrated that our algorithm could distinctively avoid problems caused by the fake solution and both the accuracy and efficiency were enhanced which made our algorithm has a bright future for further application.3. According to theory of Sobolev vector space and the discretization of Helmholtz space, the error estimate which was suitable for 3-D MT vector-finite element modeling was deduced by which the procedure of adaptive technique was guaranteed.4. Based on the fully unstructured tetrahedralization and optical strategy, the 3-D magnetotelluric h-adaptive vector-finite element method was presented through combining the error estimate. With this work, the accuracy and creditableness for 3-D MT complicatedly modeling was guaranteed.5. The 3-D magnetotelluric h-adaptive vector-finite element algorithm with unstructured mesh was implemented.

针对非结构化的四面体单元，采用坐标变换和数值积分方法，实现了MT三维矢量有限单元分析，建立起基于非结构化网格的三维MT矢量有限元计算流程，并对典型模型和国际标准电磁模型进行了数值模拟，结果对比和分析表明，基于非结构化网格的三维MT矢量有限元不仅消除了节点型有限元的伪解，而且具有很高的计算精度和速度，有广阔的应用前景。3、根据Sobolev函数的向量空间和Hemlholtz空间的分解，推导出基于残差的三维大地电磁矢量有限元后验误差估计公式，为三维大地电磁自适应矢量有限元数值模拟的实现奠定了基础。4、在完全非结构化四面体单元剖分及优化基础上，结合三维大地电磁矢量有限元后验误差估计公式，提出了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算策略，保证了对复杂大地电磁模型数值计算的精度和可靠性。5、实现了基于非结构化网格的三维大地电磁h-型自适应矢量有限元计算流程，对典型模型和国际标准电磁模型进行了数值模拟。

The research is carried on from four aspects. One is, based on answering the above open problem on a finite dimensional Euclidean space by means of partially ordered theory, to research the existence of solutions, global error bounds of proximal solutions and sensitivity of parametric unique solutions and present a class of variable-parameter three-step iterative algorithms for generalized set-valued variational inclusion problems by using - resolvent operator of set-valued mapping.Two is to consider the convexity, closedness and boundedness of the solution set of general set-valued variational inclusion problems and the sensitivity of the parametric solution set by means of graphical convergence theory. Three is to discuss directly the existence of solutions by using analytical methods for set-valued mixed quasi-variational-like inequalities and suggest a class of direct variable-parameter three-stepiterative algorithms for solving generalized set-valued variational inclusions.

研究分有三个方面：一是借助于偏序理论在有限维欧氏空间中解决了上述公开问题，在此基础上利用集值映射的η-预解算子，研究了广义集值变分包含问题解的存在性、逼近解的全局误差界、参数唯一解的灵敏性，并提出了一类变参数三步迭代算法；二是借助于图收敛理论研究了一般集值变分包含问题解集的凸性、闭性和有界性以及参数解集的灵敏性；三是用分析的方法直接讨论了集值混合拟类变分不等式问题解的存在性并提出了一类求解广义集值变分包含问题的直接变参数三步迭代算法。

Based on the load transmission mechanism of space truss, and referenced theanalysis of test materials, a formula for calculating the bearing capacity of reinforcedconcrete compression strut is introduced. By using the theory of plastic hinge-line, anupper limit solution of bent bearing capacity for four-pile cap, which coincidesprecisely with the practical measurements, is obtained. By utilizing the reaction ofthe soil under cap and by basing on the method of plastic ultimate analysis, an upperlimit solution of punching shear bearing capacity for pile cap is acquired, which. coincides precisely with the practical measurements, and the formula is similar to thecode.A brief discuss on cooperative work of strip beam of foundation and single rankof piles is made. Separately considering the pile-cap and the pile-group, thencoupling their matrix of rigidity, the inner force of pile-cap is solved by the numericalmethod under some reasonable supposition. In comparison with other method, thecalculating results are exact, reliable and convenient in using. The method provides apowerful tQol fOr further analysis and research on this kind of structure.

本文以空间桁架传力机理为基础，结合试验资料分析，推导了钢筋混凝土等边三桩承台受冲切承载力计算公式；根据塑性铰线理论，导得了与试验结果吻合良好的四桩承台受弯承载力的上限解；利用承台底土反力分布，根据塑性极限分析方法，导得了桩基承台受冲切承载力的上限解，在此基础上，通过简化假定，得到与规范公式相类似的承台受冲切承载力实用公式，该公式能方便考虑台底土反力作用，与试验结果的吻合程度比规范公式好；简要讨论了桩基条形承台梁与单排桩的协同工作分析；在一些合理假定的基础上，将承台与群桩分开考虑，分别得到其刚度矩阵后进行耦合，通过数值方法求解承台内力，算例表明，该方法结果准确，使用方便，为该类结构的进一步分析研究及工程设计提供了强有力的工具。

We use the solution on the fine-grid space to improve the accuracy of the solution.

然后再对求得的解做一次误差修正，这使得差分解的精确度提高。

We use the solution on the fine-grid space to produce a more accuracy of the solution.

最后再利用上面求得的细网格节点上的差分解对非线性项作更精确的近似，得到更加精确的差分解。

In order to facilitate the first step of the transition, the thesis defines and constructs a Domain Solution Tree, then determines the dimensions and design rules of the Design Space according to the elements of the Domain Solution Tree.

进而以测试领域为例，研究了问题空间元素（领域解题树中的各类节点）与设计空间元素之间的对应关系，为实现由分析到设计的无缝转换奠定了基础。

The orthograph can be transformed to the 3D graphics by using 3D functions in AutoCAD, thus all analysis and reasoning for the solution can be clearly visualized in 3D space, and then by baking to the 2D environment the solution can be easily made.

借助AutoCAD的三维图形功能，可将平面正投影图转化为空间三维图形，在三维空间进行分析、推理和求解，然后再返回二维作图，使解题过程概念清晰，可视性强。

Based on Euler-Bernoulli beam in elastic half space and its dynamic solution under moving loads, the solution of reaction force between ground surface and beam is presented.

用弹性半空间Euler-Bernoulli梁及其在移动荷载作用下的动力解，得到地基表面与梁之间的接触反力解答。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。