泛函分析

The problems of random nonlinear operators in Banach spaces belong to fields of random nonlinear functional analysis.

Banach 空间中的随机非线性算子问题属于随机非线泛函分析的范畴。

Nonlinear functional analysis is an important branch of mathmatics, be-cause it can explain all kinds of natural phenomena, more and more mathe-maticians are devoting themselves to it.

非线性泛函分析是数学中的一个重要分支，因其能很好的解释自然界中的各种各样的自然现象受到了国内外数学界和自然科学界的重视。

Nonlinear functional analysis is not only profound theory but also widelyused research discipline in mathematics, in the context of nonlinear problemsof mathematics and natural sciences, a number of theories and methods of dil-ing with nonlinear problems have been established.

非线性泛函分析是数学中既有深刻理论又有广泛应用的研究学科，以数学和自然科学中出现的非线性问题为背景，建立了处理非线性问题的若干理论和方法。

The whole contents is divided into five chapters. In chapter 1, as the beginning of this paper, we offered some relative knowledge, such as the cone theory and semi-order method in nonlinear functional analysis. Moreover, we established a new fixed point theorem of the mixed monotone iterative operator.

全文共分成五章：第一章作为准备知识给出了本文要用到的相关知识内容，其中包括非线性泛函分析中的锥理论及半序方法，并建立了新的混合单调算子不动点定理。

The singular differential equation has developed on the basis of nonlinear functional analysis, because it can explain a lot of natural phenomenal, more and more mathematicans are devoting their times to the study of sigular differential equation.

以非线性泛函分析为基础而发展起来的奇异微分方程理论因其能很好的解释自然界中的各种各样的自然现象而倍受关注。

And control problems such as optimal import rate control, optimal harvesting control, optimal birth control are investigated. By means of nonlinear functional analysis, differential equations, integral equations, and modern control theory, a number of research results are obtained, which are theoretically valuable and provide a solid ground for the practical use of our models.

本文系统讨论了几类年龄依赖的单种群和多种群动力系统，综合应用非线性泛函分析、微分方程、积分方程以及分布参数系统控制论等理论与方法，深入地研究了这些系统的解的存在性、唯一性以及非负有界性；研究了这些种群动力系统的最优输入率、收获率和出生率控制问题，获得了一批重要的理论成果。

Using operator theory and method of functional analysis, we study theproperties of these three frames correspondingly.

利用算子理论和泛函分析的方法，相应地对这三种框架的性质进行了研究。

Firstly, from the functional analysis, the eigenfunction series of vectorial partial differential operator is studied. The property of complete space is gotten. And this result is extended to the eigenfunction of Maxwells equations.

本文首先从泛函分析的方法出发，研究了矢量偏微分算子本征函数系的性质，得到了矢量偏微分算子正交完备归一化本征函数的存在证明，研究了Maxwell方程组的情况，证明了电磁场在均匀和非均匀介质条件下的正交本征函数系的完备性质。

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 means of the semigroup theory, spectrum theory, positive cone theory, integrated equation theory and optimal control theory, we obtain the existence of thresholds of these models, the existence and stability of the infection- free equilibrium and the endemic steady state, and the existence of optimal vaccination strategies, etc.

运用泛函分析中的半群理论、谱理论、正锥理论以及积分方程理论和最优控制理论，系统地研究了这些模型的阈值的存在性，无病平衡态和地方病平衡态的存在性和稳定性，最优接种疫苗策略的存在性等。

Since historical times,England ,where the early inhabitants were Celts, has been conquered three times .

从有历史以来，英国，在此地早期居住的是凯尔特人，已经被征服了三次。

Bluetooth OBEX File Transfer Enables the sending and receiving of files on your phone via Bluetooth.

蓝牙OBEX文件移动允许经过蓝牙传送和接受文件。。。。