多重性

Thirdly, we will concentrate on the multiplicity of the positive and minimal sign-changing solutions of the following quasilinear equations with Hardy-Sobolev critical exponent in bounded domain By Lusternik-Schnirelmann category theory, we showthe relation the number of positive solutions with the topology of the domain.

再次研究有界区域上具有Hardy-Sobolev临界指数的拟线性方程的正解与极小变号解的多重性，运用Lusternik-Schnirelmann理论，给出方程正解与区域的拓扑性质的相关性。

The copyright-infringement action must be the special the copyright infringement,because it accord with the cognizance law-standards;it favors for guarding the legal rights of the Copyrighter and cracking down on the infringement actions.

著作权侵权行为五个方面的特征是：侵权形式上的特殊性；法律适用上的严格地域性；侵权对象的多重性；侵权形式的多样性及侵权行为的隐蔽性。

The model in this paper takes the form as belowThe main contents and results in this paper are as follows:In section 1, we state our main analytical results on equilibria of the above system. First, several sufficient conditions for coexistence of the steady-state are given by the standard fixed-point index theory in cone. Second, the global structure of the coexistence solutions and their local stability are established by using bifurcation theory. Third, the multiplicity, uniqueness and stability of positive steady-state solutions to this system are derived by means of perturbation theory of eigenvalues, standard regularity theory, Sobolev embedding theorem and fixed-point index theory.

本文主要有两章内容：第一章研究了该模型正平衡解的性质，可分为三部分：第一部分运用极值原理、上下解方法和锥映射不动点指标理论得到正平衡解存在的充分条件；第二部分利用分歧理论给出了平衡态系统正分歧解的结构，并讨论了局部分歧解的稳定性；第三部分利用特征值扰动理论、标准椭圆正则化理论、Sobolev嵌入定理及指标理论讨论了正平衡解的多重性、唯一性及稳定性，并讨论了参数对解的影响。

For AIDS patients, the infections are always multiplicity, such as, bacteria, TB, epiphyte or other some virus.

对于AIDS病人来说，感染往往是多重性的，比如细菌。

Chapter 7 "Birds" and the Expressions of Poetic Nature"Flyingbirds Poems" present various and outstanding expressions ofpoetic nature by the multeity of visual angles, the abundance of theimages and the diversity of the styles.

主要表现为视角的多重性、形象的丰富性和风格的多样性，因而创作出许多各具风采的诗歌佳作。

I would say that China is a multi-faceted power.Let me explain what I mean.

在我看来，今天的中国究其实质，是一个具有多重性特征的大国。

Man can restrict his nature of self-love by his own social nature and multifold self and surpasses limits of society. Finally, man can realizes the perfection of human nature and the ends of Nature.

人能够通过其自身的社会性自然和具有多重性的自我来克制其自爱的自然，超越社会的局限，最终实现人的自然的完善和自然的目的。

It's important to note that using Multiplicity is not the same as having multiple displays for one computer.

更重要的注意，使用多重性是不一样的还要多显示器，一台电脑。

If you are a power user and have always wanted to be the master of multiple computers, Multiplicity is your answer.

如果你是一个电力用户，并一直想成为大师的多台电脑，多重性是你的答案。

All of these complexity results in the multiplicity of her personality and her special characters in the meantime.

这些复杂性影响着她性格的多重性。同时形成了她独特的叛逆性格。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。