算子方程

The operator differential equations in abstract spaces is animportant branch of modern mathematics.

抽象空间中的算子微分方程是现代数学的一个重要分支，它与数学的许多其它分支有着密切的联系，其理论对工程、力学、数。。。

This paper deals with the existence of monotone positive solutions to a type of three point boundary value problems of nonlinear second-order differential equations with p-Laplacian operator .

利用锥拉伸与锥压缩不动点定理，研究一类具 p-Laplace算子的二阶微分方程的三点边值问题单调正解的存在性，给出了单调正解存在的充分条件，并确定了解曲线的凹凸性。

In this paper, a new approach, which is based on simulated annealing algorithm for solving a class of diffusion equation of parameter operator identification of inverse problem, is presented.

文章给出了利用模拟退火算法求解一类扩散方程的参数算子识别反问题的一种新方法。

The asymptotic estimations of solution of initial value problem are obtained for Dirac equation by use of the transformation matrix operator in this thesis.

本文运用平移算子，得到了Dirac方程初值问题解的渐近估计。构造了一个整函数ω，其零点集合与具有一般两点边界条件的Dirac特征值问题的特征值集合重合。

Although some results on convex and concave iterative roots are known, there are no results about convexity for more general iterative equations. In this chapter, convexity of both increasing solutions and decreasing solutions is investigated by the divided difference theory and fixed point theory.

本章在连续函数构成的紧凸集上构造一个连续自映射算子，利用均差理论和不动点理论证明了线性型迭代方程的凹凸解的存在唯一性及连续依赖性。

As an application, the completeness of the eigenfunction system of the infinite dimensional Hamiltonian operator corresponding to a wave equation is given.

作为应用，还给出了波动方程导出的无穷维Hamilton算子特征函数系的完备性。

The book is structured so that the reader may choose parts of the text to read and still take away a completed picture of some area of differential geometry Beginning at the introductory level with curves in Euclidean space, the sections become more challenging, arriving finally at the advanced topics which form the greatest part of the book:transformation groups, the geometry of differential equations,geometric structures, the equivalence problem the geometry of elliptic operators, G-structures and contact geometry.

这本书是结构，以便读者可以选择部分文本阅读，还带了一个完整的画面，有些地区的微分几何开始入门级和曲线的部分，在欧氏空间变得更有挑战性，终于到达了高级的主题，形成了最大的一部分书：变换团体、几何的微分方程、几何结构、等价问题的几何形状，G-structures椭圆算子和接触几何。

The research of nonlinear ergodic theory began in the mid-seventies. Consequently, it got great development because it was widely used in many questions such as the numerical solution of differential equation, the existence theory of positive solution, control theory, optimization.

非线性算子半群的遍历理论的研究开始于二十世纪七十年代中期，随后由于被广泛应用于微分方程的数值解，正解的存在性理论，控制论，最优化等问题中而得到了很大发展。

Multivalued maximal monotone operator; Multivalued stochastic differential equation; Explicit solutions; Limit theorem; Denjoy's continuity; Non-Lipschitz coefficient; Large deviations

基础科学，数学，概率论、数理统计多值极大单调算子；多值随机微分方程；显式解；极限定理； Denjoy连续性；非Lipschitz系数；大偏差原理

This paper dealt with the uniform stability and the uniformly asymptotic stability of neutral functional differential equation with infinite delay .

以B空间为相空间，利用D算子的性质及Liapunov泛函方法，研究了具无穷时滞中立型泛函微分方程零解的稳定性。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。