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The proof is based on the Mountain Pass Lemma in combination with variational technique.

论文最后给出了一个具体的例子来说明主要结论的应用。

Using variational methods to discuss the number of fixed points of weakly inward mapping satisfying locally Lipschitz condition is one part of this thesis.

利用变分方法讨论满足局部Lipschitz条件的弱内向映射的不动点的个数是本文的一部分内容。

The existence and Lipschitz continuity of the J-proximal mapping are proved. By using the properties of J-proximal mapping, a class of generalized mixed variational inequalities is studied in Banach spaces. The existence and uniqueness of solutions are established.

证明了J-近似映射的存在性和Lipschitz连续性，运用J-近似映射的这些性质，研究了Banach空间中的一类广义变分不等式，提出了计算广义混合变分不等式的解的一个新的迭代算法，并进行了分析。

In chapter II, we calculate the binding energy of a quantum wire in the presence of a strong magnetic field along the wire axis by using the variational method and strong perturbation method.

在第二章中，我们用变分法和强相互作用方法计算了在一个沿着轴向的强磁场下的量子线的束缚能，讨论了束缚能随着量子线的半径，磁场和掺杂浓度的变化。

First of all, in the study from magnetohydrodynamics equilibrium equations describe the plasma derived from the balance of the Grad-Shafranov equation of the theory of expression, and to analyze its borders in a fixed way to solve the region;then we solved the equation with Variational method in given pressure, and the exact numerical value of poloidal magnetic flux and the profile of the magnetic flux surfaces contours in the definite error range are given.At last, the poloidal and toroidal magnetic field with D-shaped is obtained.

在研究中首先从磁流体力学平衡方程出发推导出描述等离子体平衡问题的Grad-Shafranov方程的理论表达式，并分析其在固定边界区域内的求解途径；然后在给定的压强分布情况下采用基于能量形式的变分法对其进行了数值计算，并在一定的误差范围内得到了极向磁通的大致图像以及等离子体的平衡位形分布；最后求出了D-型截面下的极向磁场以及环向磁场分布。

In our problem,the major term in the variational inequality isp-Laplacian.

在我们所考虑的问题中，变分不等式的主部是p-Laplace算子。

Vector variational inequalities,open mapping theorem and conjugate formulae play important roles in analysis.

向量变分不等式，开映射定理和共轭公式在分析学中都占有重要的地位，本文对这三类问题进行了研究。

Variational principles play an important role in the formulation of many problems of mathematical physics.

变分原理现在许多数学物理的表述中起着重要作用。

Variational principle is a powerful tool in many scientific aspects. It has been widely used in mathematical physics, and especially it has been successfully used in solid mechanics.

变分原理在数学物理问题中有着广泛的应用，在很多科技领域中都是一种强有力的工具，它在固体力学领域中，更是运用得卓有成效。

We construct some new iterative algorithms with errors for solving these generalized fuzzy variational inclusions by using the resolvent operator technique for maximal η-monotone mappings and prove the convergence of iterative sequences generated by the algorithms.

为了利用η-极大单调映象的预解算子技巧求解这类广义模糊变分包含，我们建立了一些新的含误差的迭代算法，并证明了由这类算法产生的迭代序列的收敛性。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。