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The main results and novelties of the paper are as follows:Firstly, we study the existence of nontrivial solution for the following nonlinear equations with singular pontential By using variational methods and critical point theory, we construct linking type critical value of this kind of singular elliptic equations, with the properties of the eigenvalue, we estimate the critical value and prove the local condition holds to show the existence of the nontrivial solution.

论文的创新点及主要结果如下：首先研究有界区域上具有奇异位势的非线性方程的非平凡解的存在性，运用变分方法与临界点理论，构造这一类奇异椭圆方程的环绕型临界值，并由特征值的性质给出临界值的估计，同时证明局部条件成立，最终证明方程非平凡解的存在性。

The variational principle of generalized potential energy is used to determine the unknown coefficients of above series. The distributions of transversal shearing and normal stresses obtained from constitutive equations and those from equilibrium equations agree with each other very well.

通过这部分的分析，得出了一个重要结论：根据该分析方法，由平衡方程与由物理方程得到的横向剪应力及横向正应力分布相当一致。

In this paper, first of all, we study the set-valued vector equilibrium problems and the set-valued vector Hartman- Stampacchia variational inequality in normed linear space.

本文首先在赋范线性空间中，研究了集值向量均衡问题和集值Hartman-Stampacchia变分不等式这两个问题的弱有效解的存在性，得到了弱有效解集的连通性和紧性结果。

The analysis of Rayleigh loss influence on optical soliton transmission is presented by peturbation, variational and numberical methods.

本文研究了存在瑞利散射损耗时对光孤子传输的影响，分别采用了微扰法，变分法及数值分析。

It is a very important numerical method for solving variational inequality and complementarity problem.

它是求解变分不等式与互补问题的一类重要算法。

In this thesis, we construct and analyze some efficient numerical methods for solving variational inequality and complementarity problem.

本文讨论了求解几类变分不等式与互补问题的有效算法。

Hence, it is meaningful to study the efficient numerical methods for solving variational inequality and complementarity problem.

因此，研究其快速数值解法是十分有意义的。

In chapter 4, we compute the symmetry group, variational symmetry group, divergence symmetry group of some operator equation.

在第四章中计算了一些偏微分算子方程的对称群，变分对称群以及散度对称群。

During the minimizing process of variational assimilation, calculation efficiencyis very important and the optimal step size greatly influences the algorithm efficiency.

在变分同化的最小化过程中，计算效率无疑是最重要的，而优化步长的计算又直接关系到算法效率的成败。

In this paper, a general, strain-consistent, third-order displacement field of shells is proposed. On this basis, the nonlinear theory of composite laminated shells including third-order transverse shear deformation and rotary inertia is developed. Hamilton's variational principle is used to derive the nonlinear static and dynamic governing differential equations and the corresponding boundary conditions of composite laminated anisotropic general shells under the orthogonal curvilinear coordinates. And the form of spherical shells is degenerated.

本文提出了一种最普遍的应变协调、三阶壳体位移场，在此基础上建立了考虑三阶横向剪切变形和旋转惯性的复合材料层合壳体非线性理论，用Hamilton变分原理导出了复合材料层合各向异性任意壳体在正交曲线坐标系下的非线性静、动力控制微分方程和相应的边界条件，并将其蜕化为球壳形式。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。