不动点定理

The existence of two positive periodic solutions and one positive periodic solution is obtained.

据我们所知，这是用锥上的Deimling不动点定理得到二阶微分系统的分支的最早的工作。

Singular boundary value problem; Fixed-point theorem; Cone; Positive solution

基础科学，数学，数学分析奇异边值问题；不动点定理；锥；正解

This article investigates the two-point boundary value problem to a coupled system of nonlinear fractional differential equations. By applying growth conditions on the nonlinear terms, we obtain an existence result of solutions. Our analysis relies on the Schauder fixed-point theorem and the reduction of the considered problem to the equivalent coupled system of integral equations.

本文讨论非线性分数阶微分方程耦合系统的两点边值问题，应用Green函数，将其转化为等价的积分方程耦合系统，并设非线性项在无穷远处有增长条件，应用Schauder不动点定理证明解而非限于正解的存在性。

Secondly, based on the different structure characteristics and additional conditions, we study several kinds of inverse problems of pseudoparabolic equations. One is a kind of pseudoparabolic inverse problem of identifying a constant coefficient solved by combining the formal solution of the problem and the additional condition properly. The second is the pseudoparabolic inverse problems of identifying an unknown boundary function and an unknown source term solved by using the Riemann function method to get the formal solution of the problem and then using the additional condition to transform the problem into a Volterra integral equation of the second kind. The third is a kind of backward heat flow problem of nonlinear pseudoparabolic equation solved by combining the Riemann function method and the fixed point theory properly.

其次，根据不同模型的结构特点和附加条件，研究了几类伪抛物型方程的反问题：一是利用问题的形式解并结合附加条件，解决了一类伪抛物型方程常数系数的反问题；二是利用Riemann函数方法获得问题的形式解，利用附加条件将问题转化成求解第二类Volterra积分方程问题，解决了一类伪抛物型方程未知边界值的反问题和未知源项的反问题；三是将Riemann函数方法和不动点定理相结合，解决了一类非线性伪抛物型方程的后向热流问题。

Chapter three deals with the controllability of a nonlinear integrodifferential systems ofSobolev type with nonlocal condition in Banach spaces. The results are obtained by using semi group theory and the Schauder fixed point theorem.

本章利用算子半群和Schauder不动点定理，在Banach空间中讨论了带有非局部初始条件的一类非线性Sobolev型积分微分系统的可控性问题。

Firstly, we analysize the boundary value problem for linear singular system, several properties for linear singular system are given, and then the existence for boundary value problem to nonlinear singular system is proved by using the previous properties discussed and Schauder's fixed point theorem.

接着，利用Banach不动点定理，研究了Volterra型广义积分微分系统边值问题解的存在唯一性，最后给出了几个推论。

Chapter 2 discuss firstly the local existence of solutions for a class of abstract functionalintegro-differential equations with unbounded delay by Schauder's fixed point theorem, then byintroducing an inequality condition and applying the continuity property of solutions it obtainsthe global existence of the solutions.

第二章先利用Schauder不动点定理讨论一类具有无限时滞抽象泛函积分微分方程解的局部存在性，然后引入一不等式条件并利用解的延拓性质获得了解的整体存在性

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 deals with a class of singular Positone boundary value problems.

对一类具有奇性Positone边界值问题进行了研究，利用非线性二择一不动点定理建立了问题正解的3个存在性原则。

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。