存在性定理

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。

Firstly, The sufficient con-ditions of the existence and uniquity of the positive equlibria by applying functional derivative isobtained; Secondly, the global attractability of the positive equlibria is investigated by charateristicroots theory and oscillation theory; Thirdly, regarding the delay as a parameter, conditions of theexistence of Hopf bifurcation and the peridic solution, furthermore, the form of the approximateperidic solution are obtained; Finally, Some specific examples are given and the solution diagrameappears by Matlab.

首先利用导数性质，得到了该模型正平衡态存在惟一性的充分条件；其次，利用特征值和振动性理论得到了该模型正平衡态全局渐近稳定性充分条件；然后，应用Hopf分支理论证明了该模型Hopf分支及近似分支周期解的存在性，并给出了周期解的近似表达式；最后，借助于MATLAB数学软件，举例并绘出了模型数值解的拟合图象，验证了文中定理条件的可行性。

The intermediate value theorem for discontinuous function is studied,the problem of discontinuous points when the left and right limit exists is considered by ZHU Le-min.

研究了非连续函数的介值定理，受朱乐敏等考虑的具有左、右极限存在的跳跃间断点的非连续函数的介值性定理的启发，利用上、下极限把介值定理推广到具有一般间断点的非连续函数的情况。

By using homeomorphism method and the extended inverse function theorem,the existence and uniqueness of the solution for the semi-linear pseudoparabolic equations is obtained.

首先在Hilbert空间中建立了强制不等式，利用同胚方法和抽象的反函数定理，得到了半线性伪抛物方程初边值问题解的存在性和惟一性定理。

The unique existence theorem for minimal determining set of completerational choice function is obtained,and the sufficient condition is used to show avery simple proof of Arrow Impossibility Theorem.

构造并证明了完全理性选择函数的最小决定集的存在惟一性定理，同时应用该定理的充分性条件给出了Arrow不可能性定理的一个简单证明。

This paper describes the content of the theorem, and theorems are given two proofs, cite the Lagrange mean value theorem in the mathematics major applications, including that inequality, identity, Limit, determine monotonicity, root The existence of such.

本文简要叙述了定理的内容，并且给出了定理的两种证明方法，例举了拉格朗日中值定理在数学中的主要应用，包括证明不等式，恒等式，求极限，判断单调性，根的存在性等。

Theorem of mean significance: The application derivative research function's nature wants directly or indirectly with the aid of Yu Zhongzhi,Specially Lagrange theorem of mean,Here is mainly from the equality proof, the inequality proof, existence asks some limits, the determination equation root and so on five aspects to carry on the discussion,so, The theorem of mean is transforms as the function in the sector research important tool, Must bring to the enough attention in the middle of ours study and the teaching.

中值定理意义：应用导数研究函数的性质都要直接或间接地借助于中值，特别是拉格朗日中值定理，这里主要是从等式的证明、不等式的证明、求一些极限、判定方程根的存在性等五个方面来进行讨论，因此，中值定理是转化为函数在区间上的研究的重要工具。在我们的学习与教学当中要引起足够的注意。

The existence of solution is studied for a class of second - order periodic boundary value problems with first applying Leray - Schauder fixed point theorem, two exislence theorems are established.

考察了一类非线性项含有一阶导数的二阶周期边值问题的解的存在性，其中非线性项是Carathèodory函数。通过构造非线性项的高度函数并且利用Leray-Schauder不动点定理建立了两个存在定理。

Using the asymptotically compact theory of Anselone' and Stepleman' theorem, the existence, the unicity , the convergence and the error estimate with O(h3) of the discrete equations are shown....

并借助Anselone的渐近紧收敛理论和Stepleman定理，证明了离散方程组的解存在性、唯一性、收敛性和精度阶O(h~3)。使用Ostrowski的不动点定理，提供了三阶收敛的迭代法。

In chapter 2, first, the index of random fixed point for random semiclosed 1-set contractive operator is investigated.

其次 讨论了随机半闭1-集压缩算子随机不动点的存在性，所获结果推广了著名的Rothe定理、 Petryshyn定理和Altman定理。

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。