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We obtain that if any 〓 is discrete or elementaryand 〓 satisfies Condition A,then the algebraic limit G of group sequence 〓is discrete or elementary.

首先,我们不再仅仅考虑离散非初等群集〓的代数极限G,而是离散群或初等群群集〓的代数极限G,我们对〓上〓变换群中斜驶元及其不动点进行了细致研究,注意到任意一个斜驶元存在一个仅仅含有斜驶元的领域,从而证明了初等群群集〓的代数极限G仍然是初等群,进而我们得到了一个代数收敛定理:如果任一〓是离散群或者初等群并且〓满足条件A,那么,群列〓的代数极限G一定是离散群或者初等群。

This paper studies a contractive mapping, obtains the existence and uniqueness of its fixed point.

该文研究了一类压缩型映射,得到其不动点的存在唯一性定理。

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。

There are some results for the problem which confine M as only related to λ. In this paper, we break down this confinement and deal with it in a wider situation. By energy estimates and fixed point method, the existence and uniqueness theorem of th...

以前的工作仅在M是参数λ的特殊情况下做的,文中打破了这种限制,在一般情况下讨论了这类非线性双曲方程的可解性,以能量估计与不动点相结合给出了此方程有惟一局部解的存在定理,从而基本上解决了这类方程初值问题的存在惟一性。

As for the existence of positive solutions, the cone theory and the fixed point index of condensing mapping are employed, and the results of the existence of positive solutions are obtained in the case of superlinear and sublinear. The conclusions extend and improve the existence theorem which Lou Ben-dong extablished in 1996 about the question of Sturm-Liouville of Banach spaces.

三、对于正解存在性问题,我们应用凝聚映射的不动点指数理论,分别在超线性与次线性情形下进行讨论,获得了一些正解存在的结果,主要结果推广和改进了1996年Lou Ben-dong对Banach空间Sturm-Liouville问题所建立的存在性定理。

Lastly, the existence theorem of three positive solutions for the boundary value problem of second-order singular functional differential equation be established by applying the index theory of fixed points in a cone.

最后,我们应用锥上的不动点指标理论建立了二阶非线性奇异泛函微分方程边值问题的三个正解的存在性定理。

We consider the existence of positive solutions of second order impulsive boundary value problems by constructing the appropriate homotopy operator and applying the theory of fixed point index in cones. our results contain the conclusion when f ≥ 0 and J_k = 0([6]). Secondly, we discuss multiple positive solutions of the following impulsive boundary

其次,我们在§2.2中讨论了下面的脉冲微分边值问题多正解的存在性在这一部分的讨论中,利用不动点指数理论,在f既非超线性又非次线性的情形下,得到了两个正解的存在性定理,把文[7]的结果推广到脉冲微分边值

The existence of positive solutions of some fourth-order singular semi-positone boundary value problems are obtained on a special cone by using the fixed point index theorem.

本文在一个特殊锥上利用不动点指数定理,得到了一类四阶奇异半正边值问题正解的存在性,并给出了一个例子作为对所获结果的应用,推广和改进了一些已知结果。

Furthermore, when the system is a periodic system, sufficient conditions are obtained that guarantee the existence, uniqueness and global attractivity of the positive periodic solution by applying the Brouwer fixed theorem and the method of constructing Liapunov function.

利用比较原理给出了系统一致持久性的充分条件;当系统是周期系统时,应用Brouwer不动点原理和构造Liapunov函数的方法给出其存在惟一且全局吸引的ω-周期正解的充分条件,并通过实例验证了文中定理条件的可实现性。

In section 2, we study the existence of sign-changing solutions of some three-point boundary value problem by the cone theory and the fixed-point index theory.

本文利用不动点指数定理研究了如下两种二阶微分方程多点边值问题变号解的存在性,同时分别得到了一个正解和一个负解。

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推荐网络例句

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm~150rpm时取得最大值,此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世,形体几无变化。

When I was in school, the rabbi explained everythingin the Bible two different ways.

当我上学的时候,老师解释《圣经》用两种不同的方法。