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The existence and uniqueness of optimal control and the corresponding maximum principle are studied by using the fixed point theorem, the Sobolev's imbedding theorem and variational principle.

本章的结论既是在已有文献中还没有见到的成果，也是对单种群动力系统最优控制问题的完善和发展。

Then,the system is linearized by variational approach,the local null controllability is proved by applying a generalized implicit function theorem and combining the property of the solution mapping.

首先得到了系统的逼近能控性；然后采用变分方法对系统线性化，再结合解映射的性质，应用推广的隐函数定理，证明系统的局部零能控性；最后给出系统零能控的结论。

Then, the system is linearized by variational approach, the local null controllability is proved by applying a generalized implicit function theorem and combining the good property of the solution mapping.

首先通过对系统线性化，构造泛函，利用对偶方程，给出控制函数具体形式的办法得到系统的逼近能控性；然后采用变分方法对系统线性化，再结合解映射好的性质，应用推广的隐函数定理，证明系统的局部零能控性；最后利用局部零能控性和逼近能控性结合给出系统零能控的结论。

Rubber ; Yeoh model ; incompressibility ; generalized ; variational principle ; FEM

橡胶； Yeoh模型；不可压缩性；广义变分原理；有限元法

But the industrialism breaks its close structure and gives birth to a variational and wizardly urban life.

工业主义打破了共同体的封闭结构，将一个变幻莫测、神奇万象的大都市生活带到了现代社会之中。

In this paper, we first introduce a class of mixed variational-like inequalities problems.

本文中，我们首先给出了一类混合似变分不等式问题。

In this paper, a numerical method to verify the existence of solutions for variational inequalities is presented.

基于文献[1]给出了一种数值证明变分不等式解的存在性方法。

In this method,without depending upon small parameter,a trial function with possible unknowns is used as initial approximation,then a correction functional is constructed by means of a general Lagrange multiplier ,which can be identified via variational theory.

本文提出了一种求解非线性方程的迭代算法，它不依赖于小参数，是先给方程一个带待定函数的试函数作为初始近似解，然后用拉氏乘子法构造一个迭代公式。

Results on existence and uniqueness of the solution for the diffraction problem are obtained by variational method and integral equation method, respectively.

考虑一类具有周期系数的Helmholtz方程，它是一类衍射光栅问题的数学模型，研究这类问题的数值解法。

The integrand in the variational principle is rewritten in symmetrical form for duality variables.

变分原理被积函数可导向对于对偶变量为对称的形式。

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。