存在性定理

In chapter 3, by Brouwer's fixed point theorem, we prove existence of the equilibrium point for high-order Cohen-Grossberg neural networks with delay, and investigate global stability of the equilibrium point by Lyapunov method.

第三章主要通过Brouwer's不动点定理证明了具延迟的高阶Cohen-Grossberg神经网络平衡点的存在性，并且用Lyapunov方法研究了平衡点的全局稳定性。

By using generalized-weak commutativity mapping, the existence of common fixed point for this class of contractive type mappings is studied in complete metric space, a common fixed point theorem for contractive type mappings is obtained, which largely improve and extend the corresponding results in some references.

通过使用映象的广义弱交换条件，在完备度量空间中研究了更为广泛的一类压缩型映象的公共不动点的存在性，给出了一个新的公共不动点定理，从而在很大程度上改进和推广了现有文献中的一些结果。

In this paper, A class of diffusion systems with nonlinear source were studied, using comparison theorem and method of upper and lower solutions .

本文利用比较定理与上、下解方法研究了一类具非线性源的扩散系统，证明了该系统整体解的存在性与零解的稳定性，推广了C。

In the third, we hit the variational principle, orthogonal decomposition, orthonormal base, Riesz representation theorem and the conjugate operators in the Hilbert space.

第三部分，Hilbert空间的变分原理、正交分解、完备标准正交系的存在性、Riesz表现定理和共扼算子等。

In this paper, the connectivity axiom and the continuity axiom in Von Neumann-Morgenstern Rational behavior axioms are weakened. Then, a set of axiom for lattice ordered decision-making behavior, which can describe the decision-making behavior more rationally, is constructed. At last, the relative unique existence theorem for utility function is obtained.

根据偏好关系所具有的格序特征，将Von Neumann-Morgenstern理性行为公理体系中的连通性公理弱化为格连通性公理，并相应地弱化连续性公理，得到了一集能更为合理地描述具有"有限理性"的决策行为的格序决策行为公理体系，构造并证明了在格序决策行为公理体系之下，效用函数的存在惟一性定理。

In Chapter 3, by using the continuity theorem of coincidence degree theory, we obtain a sufficient condition for the existence of positive periodic solutions to population models with impusives.

在第三章，利用重合度理论中的连续性定理研究了在脉冲作用下种群模型的全局周期解存在性。

Under some conditions, by using Mawhin continuity theorem and degree theory, the existence of the periodic solution of the periodic neural network is proved.

利用Mawhin连续定理以及拓扑度理论，证明了在一定条件下该周期神经网络系统周期解的存在性。

Then we use Lebesguge s dominated convergence theorem to obtain some sufficient conditions for (2) and study the existence of a bounded positive solution.

接着，利用Lebesgue单调收敛定理给出了方程(2)振动的若干充分必要条件并且研究了正有界解的存在性。

Two conservation equations are derived from a Wigner-Fokker-Planck model, they contain a third-order quantum correction term and second-order viscous term...

然后 在弱的亚音速条件下利用截断技术建立解的先验估计，在此基础上根据Leray-Schauder 不动点定理得到四阶方程弱解的存在性。

By using the theory of linear evolution systems and Sadovskii's fixed point theorem, chapter3 deals with the existence of mid-solutions,strong solutions for the Cauchy problems of neutralabstract functional differential equations dependent on time with unbounded delay, here theright function in the equations satisfies the Caratheodory conditions.

第三章利用线性发展系统理论和Sadovskii不动点定理研究了具有无穷时滞中立型时变泛函微分方程Cauchy问题mild-解、强解的存在性。其中方程的右端函数满足Caratheodory条件。

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。