指数定理

A necessary and sufficient exponential stability theorem with respect to a constant decay degree for general nonlinear dynamical systems is presented.

首先给出了一般非线性动态系统的关于常衰减度的指数稳定性充分必要定理，接着探讨了新型指数稳定性定理在线性系统稳定性分析中的应用。

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。

In the second part of Chapter 5,the supremum of real parts of characteristic roots for a nonsingular neutral degenerate retarded functional differential equation is studied.

第五章的第一部分讨论了非奇异中立型时滞方程的指数稳定性，所得的指数稳定的判定定理不同于文中的定理2。

The existence of positive solutions of some fourth-order singular semi-positone boundary value problems are obtained on a special cone by using the fixed point index theorem.

本文在一个特殊锥上利用不动点指数定理，得到了一类四阶奇异半正边值问题正解的存在性，并给出了一个例子作为对所获结果的应用，推广和改进了一些已知结果。

Motivated by this, we consider the global behavior of positive solutions of three-point boundary-value problems for second-order differential equations, under two different kinds of boundary-value problems, using fixed point theorem, fixed point index theorem and cone theory.

本文受到文献[7]的启发，运用不动点定理、不动点指数定理以及锥理论，分别研究了两种不同边值条件下二阶微分方程三点边值问题正解的整体性。

We establish the relation of inversion formulas among generalized Radon transform with known weight functions, the exponential Radon transform and classical Radon transform, furthermore obtain approximate inversion formula of the exponential Radon transform, the idea of approach above is applied to contour reconstruction and is generalized to n-dimentional euclidean space case. We discuss the support theorem, range condition of the exponential Radon transform.

本文建立了带权广义Radon变换、指数型Radon变换与古典Radon变换反演公式的关系，从而得到指数型Radon变换的近似反演公式，并且应用这种思想方法于轮廓重构，并将这一结果推广到任意维欧氏空间的情形；讨论了指数型Radon变换的支集定理及值域条件。

In fifth chapter,as applications of the existence theorem of〓-optimalcoupling operator for the jump processes,the estimate of the varied expontialconvergence rate for the jump processes and the existence of an order-preservingMarkov coupling for the jump processes are investigated,where,the obtained theexistence theorem of an order-preserving Markov coupling is a general theorem onPolish space endowed with semiorder,it includes the results that existence theoremon countable state apace endowed with total order or finite state space endow withsemiorder have been obtained by the internal and external mathematicians in recentten years.

第五章作为跳过程〓最优耦合算子存在性定理的应用，讨论了跳过程各种指数收敛速度的估计和保序Markov耦合的存在性。其中保序Markov耦合存在定理是具有偏序关系波兰空间上的跳过程最一般的定理，它包括了近10年来国内外对具有全序关系可数状态空间或具有偏序关系有限状态空间上的跳过程关于保序Markov耦合存在定理的研究成果。

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。

The aim of this thesis is to study the existence of positive solutions of boundary value problem for nonlinear second order ordinary differential equations , mainly using the fixed point index theory in a cone. The conditions of the existence of positive solutions of the boundary value problem are given in the thesis. We improve the result of the existence of positive solutions either in the sublinear or in the superlinear conditons.

本文主要利用锥上不动点指数定理，解决非线性二阶常微分方程边值问题的正解的存在性问题，并给出了边值问题正解存在的条件，改进了次线性和超线性条件下正解存在的结论。

In section 2, we study the existence of sign-changing solutions of some three-point boundary value problem by the cone theory and the fixed-point index theory.

本文利用不动点指数定理研究了如下两种二阶微分方程多点边值问题变号解的存在性，同时分别得到了一个正解和一个负解。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。