不动点定理

For a monotone twist map the well-known Birkhoff fixed point theoremsays that the circles with rational rotation number will break up whence a finitenumber of pairs of periodic points arise,half of which are elliptic and the othershyperbolic.Moreover,around each elliptic periodic point a few of new invariantcurves will appear and make a picture of phase space with a self-similar structure.Again one may ask is there a similar picture for higher dimensional Hamiltoniansystems?

对于单调扭转映射，著名的Birkhoff不动点定理指出，在通有情况下旋转数为有理数的不变曲线一般会破裂，在原来的不变曲线附近会产生有限多对周期点，其中一半是双曲的，一半是椭圆的，而在椭圆型周期点的周围又会产生一圈圈的不变曲线，使得椭圆周期点附近的动力学行为和整个相空间的动力学行为十分相象，换句话说，整个相空间具有无限嵌套的自相似结构，自然又产生了一个问题：对于自由度数目大于2的高维哈密顿系统，其相空间是否有类似的图象？

Then we prove the existence of positive solutions for difference equations by using fixed point theorem of cone expansion and compression.

另外，对非线性项具有混合单调性的情况，利用不动点指数性质及锥压缩与拉伸不动点定理等方法，得到了差分方程一个正解的存在性。

At the same time, by applying the continuous selection theorem and fixed point ...

同时，我们利用集值映像的连续选择定理和不动点定理，在拓扑矢量空间中建立了一类关于集值映像的拟平衡问题和广义拟平衡问题的平衡点的存在性定理，推广了某些相应的结果。

The present paper employs the cone theory, fixed point index theory, and Krasnoselskii fixed point theorem and ...

本文利用锥理论，不动点理论，Krasnoselskii不动点定理等研究了几类微分方程奇异边值问题解的情况，得到了一些新成果。

In this paper, to study fixed-point of compact metric space , and obtain one pair fixed-point theorems of expansion Mapping and compression Mapping.

摘要研究了紧度量空间上的不动点问题。得到扩张映射与压缩映射的不动点定理。

In this paper the existence of fixed point problems for nonlinear operator is studied; several new fixed-point theorem are established and some related known work is extended and improved.

本文研究了几类非线性算子不动点的存在性问题，建立了若干新的不动点定理，推广了前人的一些结果。

In chapter 2, by virtue of the properties of partially ordered F-type topological space, we establish some fixed point theorems of increasing mappings in this kind of space. At the same time, we investigate the existence of maximum fixed point and minimum fixed point of increasing mappings on an order interval.

第二章，利用半序F-型拓扑空间的基本性质，建立这类空间上单调增映射的不动点定理，研究其序区间上单调增映射的最大、最小不动点的存在性。

Difference equations; Green's function; Fixed point theorem; Fixed point index; Positive solutions; Cone

基础科学，数学，数学分析差分方程； Green函数；不动点定理；不动点指数；正解；锥

The equivalent characterizations of convergence of a sequence of fuzzy points in the two topological st...

在WF-模糊度量空间中建立了压缩型和局部压缩型映射的不动点理论，推广了一些重要的不动点定理； 7。

By applying a fixed pointed theorem for condesing maps, the sufficient conditions of controllability are given. This method is based on integral expression of solutions, the problem can be converted info fixed point problem of single-valued integral operators.

利用凝聚映射的不动点定理给出了一类发展包含的可控性的充分条件，处理问题的方法是基于解的积分表示，将所讨论的问题转化为集值积分算子的不动点问题。

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。