存在性定理

The existence of periodic solutions to the second order ordinary differential equation in Banach space is discussed.

本文利用半序理论，非紧性测度，凝聚映射的拓扑度，不动点定理及锥上不动点指数理论，讨论了Banach空间E中二阶常微分方程周期边值问题解的存在性，主要结果有一。

The existence of the optimal control for the system is demonstrated via compactness theorem and prior estimates.

根据预备知识，利用紧性定理和先验估计，证明了系统最优控制的存在性。

By using the compactness theorem of SBD space, Poincaréinequality onthe BD functions,we prove the existence for variational problems.

主要利用SBD函数空间的紧性定理，BD函数的Poincaré不等式等给出了变分问题的存在性。

Fourthly, Broyden iterative method is studied to solve nonlinear equation with parameters and the existence and convergence theorem is also given.

第四章的主要结果：研究用Broyden迭代求解带参数非线性方程，在弱条件下给出Broyden迭代格式的存在性和收敛性定理。

The boundary conditions are assumed to be either the Dirichlet condition or linear Robin conditions.

在第一章，我们应用上、下解方法，bootstrap技巧和Schauder不动点定理考察如下三类周期反应扩散方程组的周期稳态解的存在性和一般的时变解的渐近性态：（1）拟单增系统；（2）混拟单调系统；（3）一个非拟单调2-系统，其边界条件是Dirichlet条件或线性Robin条件。

In Chapter 1, we use the upper and lower solutions method, the bootstrap technique and the Schauder fixed point theorem to investigate the existence of periodic solutions and the asymptotic behavior of general time-dependent solutions for periodic reaction-diffusion systems of the following three types:(1) Quasimonotone nondecreasing system;(2) Mixed quasimonotone system;(3) A nonquasimonotone 2-system. The boundary conditions are assumed to be either the Dirichlet condition or linear Robin conditions.

在第一章，我们应用上、下解方法，bootstrap技巧和Schauder不动点定理考察如下三类周期反应扩散方程组的周期稳态解的存在性和一般的时变解的渐近性态：（1）拟单增系统；（2）混拟单调系统；（3）一个非拟单调2-系统，其边界条件是Dirichlet条件或线性Robin条件。

The unique existence theorem for minimal determining set of non-binarycomplete rational choice function is also obtained.

构造并证明了非二元性完全理性选择函数的最小决定集的存在惟一性定理。

Some sufficient conditions for the existence and multiplicity solutions of positive periodic solutions were obtained by using the fixed point theorem .

讨论一类具分布时滞的微分方程正周期解问题，利用锥不动点定理，获得了这类问题正解存在性和多重性的充分条件，推广和改进了已有文献的相关结果。

The main aim of this thesis is to study the properties of the maps for Heisenberg group target, which include Lipschitz and Holder continuity, L~#,H~(n , W~(1,p)#,H~(n , BMO and John-Nirenberg estimates, embedded theorems, Poincare inequalities and reverse Poincare inequalities, the regul-arities about the minimizers.

本文的主要目的是系统研究靶流形为Heisenberg群的函数及其空间的性质，其中包括Lipschitz及Hlder连续性、空间L~p及W~(1，p)的性质、空间BMO的性质及其上的John-Nirenberg估计、嵌入定理、Poincare不等式和逆Poincare不等式、能量极小映射的存在性、正则性及用调和函数逼近能量极小映射等问题。

In this paper, using Moser Twist Theorem, we obtain the existence of quasi-periodic solutions and the boundedness of solutions for Duffing equations and Liénard equation with some symmetric structure.

本文将利用Moser的扭转定理来研究Duffing方程和具有某种对称性的Liénard方程的拟周期解的存在性以及解的有界性。

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。