不动点定理

We study several fixed point problems of a class of nonlinear operator,and obtain some new results in partial order Banach space .

研究了一类非线性算子的几个不动点问题，在偏序Banach空间得到了若干新的结果作为其应用，得到了Wm ，q空间中不动点的存在性定理同时，所得的定理改进了一些文献中的主要结

It introduces normal families, including equicontinuity, Arzela's theorem, Montel's and Marty's theorems, Zalcman's lemma; univalent functions, including Koebe's and de Branges' theorems; quasiconformal mappings, including conformal length, extremal length, geometric, analytic and metric definitions, quasiconformal extension, distortion theorem, quasicircle; iteration of rational functions, including fixed points, the Fatou and Julia sets, periodic points, Siegel disks, the Hausdorff measure and dimension, etc.

具体为：正规族，包括等度连续性、Arzela定理、Montel和Marty正规定则、Zalcman引理；单叶函数，包括Koebe定理和de Branges定理；拟共形映照，包括共形模、极值长度、几何、分析和距离定义、拟共形延拓、偏差定理，拟圆周等；有理函数的迭代，包括不动点、Fatou集和Julia集、周期点、Siegel盘、Hausdorff测度和维数，等等。在教学内容上充分体现综合性、前沿性。

By using the fixed point index theorem, several sufficient conditions for the existence of at least one or infinte positive solutions are obtained.

利用不动点指数定理研究了一类二阶非线性常微分方程的三点边值问题正解的存在性问题，得到了至少存在一个或无穷多个正解的几个充分条件。

Meromorphic function, holomorphic function, normality, iterate, fixed point, periodic point, periodic cycle, composite function, shared value, unicity theorem

亚纯函数，全纯函数，正规族，不动点，周期点，周期轨道，复合函数，分担值，唯一性定理

A kind of one parameter planar singular perturbation equation is studied by the qualitative theory of ordinary differential equations, asymptotic analysis methods, implicit function theorem and fixed point methods.

本文应用微分方程定性理论、渐进分析方法、隐函数定理以及不动点理论的方法研究一类单参数二维奇异摄动系统。

Since then,by applying the Leray-Schauder continuation theorem,nonlinear alternative of Leary-Schauder,coincidence degree theory,and Krasnoselskii's fixed point theorem,many researchers have studied more general nonl...

研究了一类二阶非线性常微分方程的三点边值问题多重正解的存在性问题，在非线性项不满足超线性或次线性的条件下，利用不动点指数定理得到了至少存在两个正解的几个充分条件。

In chapter 2, first, the index of random fixed point for random semiclosed 1-set contractive operator is investigated.

其次 讨论了随机半闭1-集压缩算子随机不动点的存在性，所获结果推广了著名的Rothe定理、 Petryshyn定理和Altman定理。

Firstly in§2.1, by applying the fixed point theorem the existence of positive solutions for second-order three-point boundary value problem is discussed.

第二节，运用不动点定理研究四阶两点边值问题正解的存在性。

Main contents are as follows :In chapter one, we give a survey to the development and current state of the oscillation of differential equations and difference equations. We also introduce some preliminary material , including some basic concepts of the oscillation theory and some important fixed point theorems.In chapter two, we investigate the oscillation of second order self-conjugate differential equation with impulses.

本文由五章组成，主要内容如下：第一章概述了微分方程及差分方程的应用背景和国内、外研究状况，这一章也包括一些预备知识，如有关微分方程、差分方程理论的基本概念和重要的不动点定理。

Chapter 2 discusses the BVP of non self-adjoint nonlinear second order difference equations by applying matrix theory and Krasnoselskii fixed point theorem.

第二章利用矩阵理论与Krasnoselskii不动点定理，研究了一类非自共轭非线性二阶差分方程的边值问题。

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。