不动点方法

The whole contents is divided into five chapters. In chapter 1, as the beginning of this paper, we offered some relative knowledge, such as the cone theory and semi-order method in nonlinear functional analysis. Moreover, we established a new fixed point theorem of the mixed monotone iterative operator.

全文共分成五章：第一章作为准备知识给出了本文要用到的相关知识内容，其中包括非线性泛函分析中的锥理论及半序方法，并建立了新的混合单调算子不动点定理。

Methods Using lower-upper solution method, principal eigenvalue theory, the maximum principle and the index of fixed point of compact map in cone.

上下解方法，特征值理论，极值原理，计算锥映像不动点指数。

In third chapter, a model of step structure was introduced, and the fixed points of its Hamiltonian renormalization equations can be used to classify the different Si surfaces.

第三章首先简单的介绍了重整化群方法，然后讲述一个台阶结构的模型，它的重整化群方程的不动点可以用来区分不同的Si表面的台阶结构。

Aimed at the mathematic problem in the model of the pendulum oscillation,the paper introduces the study on the existence of odd-harmonic solutions to second order semi-linear differential equation which describes the model of the pendulum oscillation by using upper and lower solution method monotone iterative technique and the Schauder fixed point theorem respectively.

针对摆型振动模型中的数学问题，分别采用上下解方法、单调迭代法及Schauder不动点定理研究了摆型振动模型的二阶半线性微分方程奇调和解的存在性。

In Part 3, We obtain the existence of positive solutions of semilinear evolution impulsive differential equations under the suitable conditions by using the same method. And example is given to illustrate main result.

我们采用相同的方法利用抽象锥上的不动点定理，在合适的条件下获得正解的存在性，并构造例子说明所得结果的应用。

This paper was concerned with the Dirichlet-Neumann mixed boundary value problem of bipolar quantum hydrodynamic model in thermal equilibrium. By truncation method and Leray-Schauder fixed point theorem, the existence of solution to the problem is proved. In addition, the uniqueness of the solution was proved as the Plank constant was large enough.

研究了热平衡状态下双极量子流体动力学模型的Dirichlet-Neumann混合边值问题，利用截断方法和Leray-Schauder不动点定理证明了其解的存在性，另外还证明了当普朗克常数充分大时其解是唯一的。

InSection 2,we give several sufficient conditions for the existence of one solution,multiplesolutions and infinitely many solutions of the Sturm-Liouville bvps via the generalizedpolar coordinates.Then in Section 3,the existence of positive solutions are proved undersuperlinearity,sublinearity and many other conditions by a fixed point theorem in cones.Our results have generalized those in many articles.A detailed discussion of periodic solu-tions of a kind of functional differential equations with high-order Laplacian-like operatorcan be found in Section 4 and this subject has not been studied before.

在第二节，我们定义了一种新的坐标变换-广义极坐标，并利用它讨论了p-Laplacian算子和Laplacian-型算子的Sturm-Liouville边值问题，分别得到了存在一个解、多个解、无穷多个解的多个充分条件；第三节研究p-Laplacian算子的Sturm-Liouville边值问题正解的存在性与多重性，采用的是锥上的不动点定理，全面推广了这一方面已有的结果；对目前研究较少的高维Laplacian-型算子及带有Laplacian-型算子的泛函微分方程的周期解问题，我们在第四节做了一些研究，这也是拓扑方法的一个应用。

Periodic fluid pulsation in aeroplane hydraulic piping could induce fluid-construction vibration and lead to fatigue damage. It is impossible to find the error sensor's optimization location because of the pressure standing wave, and the pulsation attenuation effect is not perfect when adopting pulsation attenuation at single point. For this reason, a distributed active control method of fluid pulsation was presented. To avoid stationary point in all aviation states, several fluid pulsation actuators and error pressure sensors were placed along the piping. The second fluid pulsation produced by actuators can counteract the primary pulsation brought by aviation piston pump and make the mean pulsation of whole piping minimum when adopting adaptive feed- forward control and the filtered-X least mean square algorithm.

针对飞机液压能源管路系统中的周期性流体脉动诱发流固耦合振动，导致管路疲劳损伤的问题，针对管路中存在压力驻波特性，在采用单点消振时寻找误差传感器最佳布局位置困难而引起脉动抑制效果不理想的缺点，提出了一种分布式流体脉动主动控制方法，即沿管路不同位置布置多个主动消振阀和误差压力传感器，在任意飞行阶段，避开压力驻波点，以误差压力传感器的脉动测量值为控制目标，采用一种针对周期脉动主动控制的自适应前馈控制法和多通道自适应滤波－X LMS算法，调整控制器参数，使主动消振器产生的次级脉动与管路中的初始脉动相互抵消，达到整个管路中的平均流体脉动最小的效果。

Existence Result for Semipositone Second-Order Three-Point Boundary Value Problem

利用不动点指数结合平移变换的方法，研究了一类四阶奇异半正边值问题，得到了其C~2[0，1]∩C~4(0，1)正解存在的一个新结果。

One of multiple modes of the governing equation was obtained using Galerkin s method to obtain a parametrically excited Duffing s oscillator,and the fixed points and homoclinic orbit s .

用Galerkin方法将系统简化为参数激励和强迫激励耦合的单模态Duffing振子，得到了系统的不动点和同宿轨道。

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。