不动

Among many directions of the fixed point researches, it becomes main problem that the convergence problem about making approximating fixed point sequences and its application in control, nonlinear operator and derivative equation etc. The research of this problem will play an important role in its application in reality.

在不动点问题研究的众多方向中，关于构造渐近不动点序列的迭代收敛问题以及其在控制、非线性算子和微分方程等方面的理论结合及应用成为研究的主流问题，对这方面问题的研究会在实际运用中起到至关重要的作用。

This paper sets up the fixed point theorems for cone stretching or compression and more extensive fixed point theorems for cone stretching or compression in their normal forms on the condensing mapping.

本文建立凝聚映象的锥拉、压不动点定理和更为广泛的范数形式凝聚映象的锥拉、压不动点定理以及对非锥映象的表现形式，然后利用所得的结果来研究凝聚算子的固有值的全局特征和算子方程的非零解并用到YpbIcoH算子上。

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。

In this project,we primarily investigated the growth of solutions of some types of differential equations,and the hyper order,the exponents of convergence of zeros and fixed points of solutions with infinite order, especially, expononts of convergence of fixed points of first, second order derivatives and differential polynomials of solutions.

中文摘要：在本项目中，重点研究了几种类型的微分方程解的增长性，及无穷级解的超级，零点收敛指数，不动点收敛指数，特别是解的一阶，二阶导数及微分多项式的不动点收敛指数。

In this paper, we mainly apply theory of ordering in nonlinear functional analysis, cone theory, topological degree theory, cone expansion and compression theory, and the method of upper and lower solutions, partial ordering method, iterative method to study some nonlinear differential equations BVP and fixed points problems of mixed monotone operators, and obtain some new results.

中文摘要：在本文中，我们主要应用非线性泛函分析中的半序理论，锥理论，Leray-Schduder拓扑度理论，锥拉伸与锥压缩不动点理论，以及上下解方法，半序方法，迭代方法对一些非线性微分方程边值问题和混合单调算子的不动点问题进行讨论，并得到了一些新成果。

By using the cone and partail ordering theory, and mixed monotone operator theory in nonlinear funtional analysis, the existence and uniqueness of the common fixed point for two non-monotone binary operator are discussed in partial ordering Banach space.

利用锥与半序理论和混合单调算子理论，讨论了半序Banach空间中两个非单调二元算子的公共不动点的存在性和唯一性，并给出了迭代序列收敛于公共不动点的误差枯计，所得结果是某些已知结果本质改进和推广。

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

With complex analytical analysis for B, the fixed points of B at real axis and C-plane are found. It is proved that zero is the only attract fixed point and the iteration of B on the complex plane is symmetrical. And the domains of the constringency and the divergence of B are given.

通过对B的复解析分析，得出了B在实轴和复平面上不动点的性质与求解方法，证明了0点为唯一的吸引不动点；说明了B在复平面上迭代的对称性，求出了函数迭代在整数点处的敛散区域。

This paper has further extended these conclusions on the foundations of them and obtained some new results with the method of Hulwize Theorem, Schauder Fixpoint Theorem and Tapered Fixpoint Theorem.

本文主要是在这些结果的基础上将已有的结论作了进一步的推广，利用了霍维茨定理、Schaudr不动点定理、锥上不动点定理等得到一些新的理论。

Revive: it may wrest the screw cap due to the rust. It shall be used when installation.

缓解：能缓解因锈蚀而拧不动的螺帽，使它容易拧下来，为了防止将来拧不动，在安装时就使用它。

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。