不动点方法

The reference domain is assumed to be a bounded open set of R~N with boundary Γ of class C~2. We investigate in this paper the null controllability for the semilinear parabolic equations in non-cylindrical domains. The fixed point method is used in the proof.

本文讨论了定义在上述非柱形区域中的半线性抛物方程零能控性，我们使用的方法主要是通过同胚映射将非柱形区域中的抛物方程转化为柱形区域中的抛物方程，再利用不动点方法得到半线性抛物方程的有关结果。

Using the change of variable and fixed point method andmethod of approximation, we obtain some interesting and new results on the existenceand uniqueness of bounded solutions and almost periodic solutions of these equations.

利用变量替换和不动点方法及逼近法，我们得到了此类方程有界解和概周期解的存在性及唯一性的一些有趣的新结果。

In this paper, we will discuss the existing condition of the periodic solution of Duffing type equation with damping term. We use homeomorphism and fixed point method to prove the periodic solutions existence. We try to loose its condition, analysis and then get the existing condition of periodic solution according to defining atmospheric dynamics equation.

本文中，我们探讨带阻尼项的Duffing型方程周期解的存在性条件，运用不动点方法和Leray-Schauder度理论来证明其存在周期解，尽可能放宽其约束条件，并针对具体的大气动力学方程，分析并求取其周期解的存在性条件。

By a fixed point method,we prove local existence and uniqueness.

利用压缩映射不动点方法证明了局部解的存在唯一性。

The convergence of the traditional nonlinear equations is related to the selected initial value, but the convergence of the fixed point method is not related to it.

传统的非线性有限元方程组的数值求解法（牛顿-拉普森迭代法与共轭梯度法）只能求解单值性有限元方程，且其收敛行为与初始值的选择有关，而不动点方法在求解非线性方程组时的收敛行为不受初始值选择的影响，在大范围内是一致收敛的。

Nonlinear hyperbolic equation ; energy estimation ; fixed point method ; local solution

非线性双曲方程；能量估计；不动点方法；局部解

Bounded ; solutions ; Almost periodic sofutions ; Fixed point method

有界解；概周期解；不动点方法

The positive periodic solution of functional differential equation with infinite delay is deeply concentrated these years, some scholars study this subject by means of Lyapunov theorem, Schauder fixed point theorem, and cone extending and compression theorem (from thesis -[5]), and they obtain the existence theorem of positive periodic solution.

近年来，无穷时滞泛函微分方程的周期解问题受到广泛关注，一些学者应用Lyapunov泛函方法，Schauder不动点方法，以及非线性泛函分析中的锥拉伸锥压缩方法(见[1]-[5])，研究了无穷时滞泛函微分方程的周期解的存在性问题。

In Chapter 3 Firstly, the exponential stability in mean square and almost sure exponential stability for neutral stochstic neural networks with time-varying delay can be discussed by using the linear matrix inequality and the semimartingale convergence theorem; And our sufficient conditions are less conserative; Secondly, by utilizing the fixed point theorem, some sufficient and necessary conditions ensuring the asymp- totic stability in mean square for neutral stochastic neural networks with time-varying delays can be given.

第三章首先，利用线性矩阵不等式方法和半鞅收敛定理，考虑了一类具变时滞中立型随机神经网络的二阶矩指数稳定性和几乎必然指数稳定性，所得到的条件保守性要好；其次，采用不动点方法，给出了具变时滞中立型随机神经网络的二阶矩渐近稳定性的充要条件。

In chapter 2, By combining the theory of exponential dichotomies of linear system and the method of functional analysis, some sufficient conditions that guarantee the existence and uniqueness of periodic solution of the systems are obtained.

第四章，考虑具有无穷时滞的非线性积分微分方程概周期解的存在性和唯一性问题，利用矩阵测度和不动点方法获得了一类方程的概周期解的存在性与唯一性的充分条件。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。