查询词典 existence theorem

In addition also introduced the differential theorem of mean in the proof equality and the inequality, the certificate equation root existence, asks the limit, to ask the approximate value, as well as aspect and so on research function condition should thus deepen to the differential theorem of mean understanding.

此外还介绍了微分中值定理在证明等式和不等式、证明方程根的存在性、求极限、求近似值，以及研究函数性态等方面的应用，从而加深对微分中值定理的理解。

In this paper, we use the coupled fixed point theorem for mixed monotone condensing operators to obtain an existence, uniqueness and iterative approximation theorem of solutions of initial value problems for second order mixed monotone type of impulsive differential equations.

利用混合单调凝聚算子的耦合不动点定理，给出了二阶混合单调型脉冲微分方程的初值问题的解的存在唯一性及迭代逼近定理。

In this thesis, we take the delay r as a bifurcation parameter to investigate the Hopf bifurcation phenomenon in system (1). By analyzing the associated characteristic transcendental equation of system (2), and using the Hopf bifurcation theorem, we obtain one condition for the existence of Hopf bifurcation in system (1). Furthermore, based on the center manifold theorem and the method of normal form, some interesting results about the properties of Hopf bifurcation are obtained, including the direction of Hopf bifurcation and stability of Hopf bifurcating periodic solutions.

我们以时滞T作为分支参数，研究了系统(1)的Hopf分支现象：通过分析系统(2)的特征超越方程，结合利用Hopf分支定理获得了系统(1)的Hopf分支存在的一个条件；利用中心流形定理和正规形方法分析了系统(1)的Hopf分支的性质，包括分支的方向和分支周期解的稳定性。

Firstly, we prove the existence and uniqueness of the adapted solution of multi-dimensional backward stochastic differential equations driven by Brownian motion and Lévy process by using predictable representation theorem and the fixed point theorem about contract mapping, and also prove the comparison theory.

第一部分运用可料表示定理和压缩映射原理证明由布朗运动和Lévy过程共同驱动的多维倒向随机微分方程适应解的存在唯一性及其相应的比较定理。

Secondly in§3.2 ,firstly we prove a new fixed point theorem on Banach space,and study the Sturm-Liourille boundary value problem with the theorem and some properities of concave function, then the existence of three positive solutions is gotten.

第二节，先证明一个新的锥上不动点定理，再利用此定理及凹函数的性质来研究边值问题，得到了三个正解的存在性。

Secondly, based on the Mawhin's continuity theorem in coincidence degree theory and the Brousk's theorem, some novel criteron of the existence on periodic solutions are obtained under the more generalized assumptions than before.

主要工作是：第一，应用构造Liapunov函数以及Lasalle不变性原理，给出了解的有界性与收敛性的一些新的充分条件和充分必要条件，这些结果包含或扩展了已有文献关于同样问题的一些重要结果。

Under suit upper and lower solution, iteration sequences were constructed, and existence and unique of solutions of linear boundary value problems on second order nonlinear Hammerstein type integro-differential-difference equation were obtained by means of applying the Arzela-Ascoli theorem Lebesque control convergence theorem and disproof method.

在上下解存在的条件下，构造迭代序列，由Arzea-Ascoli定理和Lebesque控制收敛定理得到了二阶非线性Hammerstein型积分微分差分方程的线性边值问题的解的存在性。再利用反证法获得了解的唯一性。

We discussed the coupled generalized BBM equations with pseudodifferential operator in Chapter three.In this chapter we get the global existence for the Cauchy problem by Banach-fixed point theorem ,a priori estimates and Sobolev embedding theorem.

第三章讨论了具拟微分算子的广义BBM方程组，通过Banach不动点定理、解的先验估计和Sobolev嵌入定理得到了解的整体存在性。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先，第二章在非Lipschitz条件下，研究了第二类方程的解的存在唯一性问题，在此基础上，又证明了解的稳定性；第三章在非Lipschitz条件下，证明了第二类BSDE解的比较定理，并在此基础上，利用单调迭代的方法，构造性证明了最大、最小解的存在性；第四章在以上的一些理论基础之上，得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果，主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的，得到了最优控制和动态规划的一些结果，在这一章的最后还讨论了相应的效用函数的性质，如，效用函数的单调性、凹性以及风险规避性等；第五章，针对第一类倒向随机微分方程，运用单调迭代方法，证明了最大和最小解的存在性，并研究了解的其它性质及在效用函数上的应用。

The process of our study links some of the most basic questions about C〓 with beautiful classical results from analyticfunction theory. For instance, it is essential Littlewood subordination theorem that assures that composition operators act boundedly on many analytic function spaces. And there are close connections between the compactness of C〓 and the existence of angular derivatives of ψ at points of 〓D. It involves the classical Julia-Careatheodory theorem, Denjoy-Wolff theorem and Nevanlinna counting functions and so on. It makes many old theorems in analytic-function theory getting some new meanings, and bestows upon functional analysis an interesting class of linear operators. This thesis consists of six chapters as follows: Chapter 1 is a preparatory in nature.

从而建立了C〓的算子性质与解析函数论中许多漂亮的经典结果之间的联系，如许多解析函数空间上复合算子的有界性本质上往往是著名的Littlewood从属原理，复合算子的紧性与其诱导映射在边界〓D上的角导数之间有着紧密的联系等等，这样自然而然地涉及到经典函数论中的Julia-Caratheodory定理，Denjoy-Wolff定理及Nevanlinna计数函数等等一些结果，并以此赋予函数论中许多古老问题以新意，同时也为泛函分析提供了一类十分具体的线性算子。

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。