不动点定理

In this paper,we discuss the existence of positive solution for singular positive boundary value problem of second order differential equations by using a general cone fixed point theorem .

利用一个普通的锥不动点定理研究了二阶奇异非共振边值问题正解的存在性。

We introduce a set of real functions H, and use to it to give a fixed point theorem of tother type for complex mappings on complete metric spaces, which improves and generalizes the corresponding results on compact metric spaces or under the condition of weakening compactness obtained by Fisher, Telci and Xu Xiao-li, respectively.

利用引入的实函数类H，在完备度量空间上给出了复合映射的另一种类型的不动点定理，改进并推广了Fisher、Telci和徐晓立等在紧致度量空间上或在弱化紧性条件下得到的相应结果。

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。

At first, using fixed point theorem, we establish the sufficient conditions which guarantee the existence, uniqueness, uniform stability of periodic solutions for the equations.

首先，我们利用不动点定理，建立了保证该类方程周期解的存在性、唯一性及一致稳定性的充分条件。

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。

The existence of mild and strong solutions of a nonlinear integrodifferential systems of Sobolev type with nonlocal condition in Banach spaces is discussed.

本文利用算子半群理论和Schauder不动点定理在Banach空间讨论了一类带有非局部条件的非线性Sobolev型积分微分系统的适度解和强解的存在性。

We prove the existence of integral solutions for semilinear integrodifferential equations with nonlocal conditions in Banach spaces.

运用预解算子理论和Schauder不动点定理，在Banach空间证明了一类非局部半线性积微分方程积分解的存在性。

This chapter deals with the existence of mild and strong solutions of a nonlinear integrodifferential systems of Sobolev type with nonlocal condition in Banach spaces.

本章在Banach空间中，用算子半群理论以及Schauder不动点定理讨论了一类非线性Sobolev型积分微分方程，在非局部初始条件下，适度解和强解的存在性。

By using the Krasnoselskii fixed point theorem, an existence result of two positive solutions is obtained under suplinear condition and sublinear condition.

讨论一类四阶非线性微分方程组Dirichlet边值问题正解的存在性，利用Krasnoselskii不动点定理得到这类边值问题在超线性和次线性条件下至少存在两个正解。

In chapter 3, as a application of fixed point theorems in gauge spaces, by using the results in chapter 2 we study the existence and uniqueness of solution for integral equation of Voletrra type in C.

第三章，作为度规空间中的不动点定理的应用，我们利用第二章中的结果，在C空间中研究了Voletrra型积分方程解的存在性与唯一性。

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。