不动点方法

Up to now, only a few papers consider singular differential equations in abstract space.

增算子不动点理论以及建立在其基础之的上下解方法是研究各种非线性问题时经常使用的基本方法之一。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

ABSTRACT Fractal image coding, which is also called attractor image coding, is a emergent method of image compression during the last decad...

分形图像编码方法是近十年来诞生并发展起来的一种新型图像压缩方法，它将图像编码为一组收缩映射，由这组收缩映射的不动点近似待编码对象。

We analyse and compare the traditional timemarching method, the fixed point iteration method, Chan, Chan and Zhou proposed such an approach using the Newton method combined with continuation and the primal-dual method.

本文对传统的时间依赖方法，不动点迭代法，原始对偶方法，Zhou，Zhou和Chan提出的牛顿法与延拓法相结合的方法进行了比较分析。

Chapter two mainly considers the periodic boundary value problems for impul-sive differential equations. Some existence results, obtained by the help of Schaeffers fixed point theorem and the method of upper and lower solutions coupled with the monotone iterative technique.

第二章讨论了两类周期边值问题，通过利用Schaeffer不动点定理，上下解方法和单调迭代方法，建立了解存在的充分条件。

By measuring the distance between the stable manifold and the unstable manifold of the hyperbolic fixed point in the Poincare map, it is shown whether the system has transversaUy homoclinicpoints and chaos in the sense of Smale horseshoes.

Melnikov方法是用来判定一个系统是否存在Smale马蹄意义下的混沌的一种有效的数学方法，它通过测量Poincare映射的双曲不动点的稳定流形与不稳定流形之间的距离来判定系统横截同宿点的存在性及Smale马蹄意义下的混沌的存在性。

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。

In studing methods,partial func-tional differential equations sum up the theories and methods of ordinary differentialequations,partial differential equations,the semigroup theory and the fixed-pointtheory in functional analysis and the basic concepts,theories and methods suit-able for the partial differential equations with delay are formed.

偏泛函微分方程在研究方法上综合了常微分方程的理论方法和泛函分析中算子半群、不动点理论以及偏微分方程的理论方法，并形成了以时滞为基本特征的泛函微分方程的基本概念、理论和方法。

By using Schauder fixed point theorem and upper and lower solution method,we ob- tain some new existence criteria for positive solution to a singular p-Laplacian BVPs with sign-changing nonlinearity involving derivative.

借助于上下解方法和Schauder不动点定理，建立了测度链上非线性项变号的奇异p-拉普拉斯多点边值问题正解的存在性准则。

The adaptive canted method is applied to the chaos control of two-dimensional multiparameters Cournot model.

将自适应控制方法应用到二维多参数的古诺生产模型，其控制目标是通过对控制参数的小扰动将系统引导到不稳定不动点或均衡点。

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。