不动点定理

The boundary value problem for first-order differential equations with a parameter refers to the finite solution condition of equation which includes unknown quantity and its first-order derivative that not only relies on interval value but also relies on the parameter of the equation,which is always settled by fixed point theory or successive approximation method.

含一个参数的一阶微分方程边值问题是指：含有未知量及它的一阶导数的方程的定解条件不仅依赖于在区间端点的取值，而且依赖于方程中的参数。通常它用不动点定理或逐步逼近法来解决。

In addition, the applications of the directional derivative and differential of the fuzzy mappings from 〓 to Ein convex fuzzy programming, the applications of the fixed point theorems of increasing fuzzymappings in fishery production and the applications of the integral over a directional linesegment of the fuzzy mappings are also studied.

另外，还给出了从〓到〓的模糊映射的方向可导性及可微性在凸模糊优化中的应用、增模糊映射的不动点定理在鱼业生产中的应用及模糊映射在有向线段上积分在获取统计数字方面的应用。

The boundary conditions are assumed to be either the Dirichlet condition or linear Robin conditions.

在第一章，我们应用上、下解方法，bootstrap技巧和Schauder不动点定理考察如下三类周期反应扩散方程组的周期稳态解的存在性和一般的时变解的渐近性态：（1）拟单增系统；（2）混拟单调系统；（3）一个非拟单调2-系统，其边界条件是Dirichlet条件或线性Robin条件。

In Chapter 1, we use the upper and lower solutions method, the bootstrap technique and the Schauder fixed point theorem to investigate the existence of periodic solutions and the asymptotic behavior of general time-dependent solutions for periodic reaction-diffusion systems of the following three types:(1) Quasimonotone nondecreasing system;(2) Mixed quasimonotone system;(3) A nonquasimonotone 2-system. The boundary conditions are assumed to be either the Dirichlet condition or linear Robin conditions.

在第一章，我们应用上、下解方法，bootstrap技巧和Schauder不动点定理考察如下三类周期反应扩散方程组的周期稳态解的存在性和一般的时变解的渐近性态：（1）拟单增系统；（2）混拟单调系统；（3）一个非拟单调2-系统，其边界条件是Dirichlet条件或线性Robin条件。

With the method of upper and lower solutions,its associated monotone iterations and the fixed point theorem,the coexistence solutions to a strongly coupled elliptic system are studied.

采用上下解及相应的单调迭代序列的方法，结合Schauder不动点定理，研究带Dirichlet边界条件的两种群的互惠模型强耦合问题共存解。

In the second part, we make use of fixed point theorem of conic expansion and compression to prove the existence of two positive solutions in Banach spaces for ...

第二部分利用锥拉伸与压缩不动点定理证明了Banach空间中非线性项系数带变号的二阶四点边值问题两个正解的存在性。

In addition, when the nonlinearities have the properties of mixed-monotonicity, the existence of a positive solution for difference equations is ob-tainded by using fixed point theorem in a cone or fixed point theorem of conic expansion and compression.

在最后一部分讨论了带有特征值的非线性二阶差分方程正解存在性问题，利用锥压缩与拉伸不动点定理及逼近性理论，在一定的假设条件下，得到了差分方程正解存在性。

In this paper, the almost periodic solution for a class of two-degree-of-freedom nonlinear oscillating systems is studied by using the Leray-Schauder fixed point theorem and the method of Liapunov function.

运用Leray-Schauder不动点定理和Liapunov函数方法，研究了一类两自由度非线性振动系统的概周期解，得到了该振动系统概周期解存在的充分条件。

Chapter two mainly considers the periodic boundary value problems for impul-sive differential equations. Some existence results, obtained by the help of Schaeffers fixed point theorem and the method of upper and lower solutions coupled with the monotone iterative technique.

第二章讨论了两类周期边值问题，通过利用Schaeffer不动点定理，上下解方法和单调迭代方法，建立了解存在的充分条件。

The sufficient conditions for guaranteeing the permanence of the system and the existence and uniqueness of periodic solution having globally asymptotical stability are obtained by using the extremum principle,fixed point theorem and V function method s together.

讨论一类具 Holling 类功能反应和放养的捕食链非自治扩散系统，应用极值原理和不动点定理及 V函数法，得到该系统的一致持久性以及存在唯一全局渐近稳定周期解的充分条件。

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。