不动点方法

The solutions are obtained for both the steady-state case and the developing case by the fixed point theorem and the semi-discretization method.

通过不动点理论结合半离散方法，分别得到定态情形和发展方程解的存在性。

Since they are based on Banach fixed point theorem to construct the local solution.

这两种方法都是用Banach不动点定理构造局部解。

The third section is the main part of this paper, where we discuss the existence of positive entire solutions by the super-subsolution method and some fixed point theorem.

第三章是本文的主要部分，主要用上下解方法和不动点定理解决解的存在性问题，推广了已有的成果。

I asa natural extension of the classical Newton method,based on a generalizedKakutani fixed point theorem,is presented that is well-defined.

方法I是经典牛顿法的自然推广，它的适定性是基于一个广义的Kakutani不动点定理得到的。

The tools used in this thesis are global structure, the cone theory and the fixed point index.

本文采用的方法主要是全局结构，锥理论和不动点指数。

Some new methods of computation for random fixed point index of random 1-set-constractive operator.

利用锥理论给出了随机1-集压缩算子的随机不动点指数的一些计算方法。

Furthermore, when the system is a periodic system, sufficient conditions are obtained that guarantee the existence, uniqueness and global attractivity of the positive periodic solution by applying the Brouwer fixed theorem and the method of constructing Liapunov function.

利用比较原理给出了系统一致持久性的充分条件；当系统是周期系统时，应用Brouwer不动点原理和构造Liapunov函数的方法给出其存在惟一且全局吸引的ω-周期正解的充分条件，并通过实例验证了文中定理条件的可实现性。

The forth algorithm is the same as the third one with an addition of finite termination criteria. Although the latter two algorithms have only linear rate of convergence, they are especially suitable for large-scale and sparse problems, with features of simple formula, small storage, sparsity preservation and easy implementation.

前者借助NCP函数把互补问题转化为等价的非光滑方程组，再用带参数的光滑方程组近似这些非光滑方程组，最后用牛顿型方法求解所得到的光滑方程组，希望通过光滑参数趋于零得到原来互补问题的解；后者基于等价不动点格式，构造了一个光滑迭代算法和一个具有有限终止性质的算法，虽然这种迭代算法仅有线性收敛速度，但由于其格式简单、存储量小、保稀疏性、非常易于计算机实现等特点，故较适用于求解大规模稀疏问题。

Using variational methods to discuss the number of fixed points of weakly inward mapping satisfying locally Lipschitz condition is one part of this thesis.

利用变分方法讨论满足局部Lipschitz条件的弱内向映射的不动点的个数是本文的一部分内容。

The second section: Under the conditions of nonlinear boundary controbility, we consider the initial boundary value problem of Camassa—Holm equations with dissipative. By using the contractive mapping fixed point theorem and a priori estimates, the existence of global smooth solution, global attractor in H〓, time periodic solution or almost-periodic solution and the global exponential stability are proved.

第二部分：在非线性控制边界条件之下，对于带耗散项的Camassa—Holm方程的初边值问题，用压缩映射不动点原理及先验估计方法，证明了整体光滑解的存在性、整体解的指数稳定性、H〓空间中整体吸引子的存在性以及时间周期解和殆时间周期解的存在性。

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。