不动点定理

Main foundation is the approximation theorem of completely continuous operators and the Guo-Krasnosel' skii fixed point theorem of cone expansion-compression type.

主要工具是全连续算子的逼近定理和锥拉伸与锥压缩型的Guo-Krasnosel' skii不动点定理。

In this paper, we use the coupled fixed point theorem for mixed monotone condensing operators to obtain an existence, uniqueness and iterative approximation theorem of solutions of initial value problems for second order mixed monotone type of impulsive differential equations.

利用混合单调凝聚算子的耦合不动点定理，给出了二阶混合单调型脉冲微分方程的初值问题的解的存在唯一性及迭代逼近定理。

By using the integral equation and the Schauder fixed point theorem, through considering the height of nonlinear term on some bounded set, a new existence theorem is established.

利用积分方程和Schauder不动点定理，通过考察非线性项在某些有界集合上的高度建立了一个新的存在定理。

Secondly in§3.2 ,firstly we prove a new fixed point theorem on Banach space,and study the Sturm-Liourille boundary value problem with the theorem and some properities of concave function, then the existence of three positive solutions is gotten.

第二节，先证明一个新的锥上不动点定理，再利用此定理及凹函数的性质来研究边值问题，得到了三个正解的存在性。

First we give some necessary and sufficient conditions for the oscillation of(1) by Lebesguge s dominated convergence theorem and Schauder — Tychonoff fixed point theorem.

这篇文章中，我们首先利用Lebesgue控制收敛定理，以及Schauder-Tychonoff不动点定理给出了方程(1)振动的若干充分必要条件。

We discussed the coupled generalized BBM equations with pseudodifferential operator in Chapter three.In this chapter we get the global existence for the Cauchy problem by Banach-fixed point theorem ,a priori estimates and Sobolev embedding theorem.

第三章讨论了具拟微分算子的广义BBM方程组，通过Banach不动点定理、解的先验估计和Sobolev嵌入定理得到了解的整体存在性。

By using of the decomposition of equation and the Leray-Schauder fixed point theorem, four existence theorems are established.

通过使用方程的分解技巧和Leray-Schauder不动点定理建立了4个存在定理。

On the base that two comparison theorems are established,applying the fixed-point theorems,we investigate the existence of maximal and minimal solutions forfirst order initial value problem and the JKjperiodic boundary value problem of discontinuous differential-integral equations of mixed type in partial-ordered Banach spaces,respectively.

在建立了两个比较定理的基础上，我们应用不动点定理，分别研究了半序Banach空间中不连续的一阶混合型微分-积分方程的初值问题与周期边值问题最大解与最小解的存在性。

By means of a nonlinear alternative theorem of Leray-Schauder type and Guo-Krasnoselskiis fixed point theorem in a cone, we establish the existence theorem of a positive solution to a singular coupled system of nonlinear fractional differential equations.

借助于锥上的非线性Leray-Schauder择一型定理和郭-Krasnoselskiis不动点定理，我们建立了非线性奇异耦合分数次微分方程组正解的存在性定理。

By means of a nonlinear alternative theorem of Leray-Schauder type and Guo-Krasnoselskii's fixed point theorem in a cone, we establish the existence theorem of a positive solution to a singular coupled system of nonlinear fractional differential equations.

借助于锥上的非线性Leray-Schauder择一型定理和郭-Krasnoselskii's不动点定理，我们建立了非线性奇异耦合分数次微分方程组正解的存在性定理。

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。