查询词典 fixed point theorem

The purpose of this part is to study the delay differential systems in Banach space using the method of fixed point theorem.

一方面在非时滞的情况下通过构造比较函数，利用Brouwer不动点定理得到非时滞微分方程正周期解的存在唯一性，及周期解全局吸引的充分条件。

In Chapter 2, we use Zorn lemma and generalized order set general principle [47] to generalize classical Caristi fixed point theorem, respectively, which weaken the condition that the functional is bounded from below.

在第二章中，我们首先分别利用Zorn引理和推广的序集一般原理[47]推广了古典的Caristi不动点定理，削弱了泛函下方有界这个条件。

According to that Caristi fixed point theorem is equivalent to Ekeland variational principle, we weaken the condition that the functional is bounded from below in Ekeland variational principle, then we enlarge the area of the applicable functionals.

鉴于Caristi不动点定理和Ekeland变分原理的等价性，我们对Ekeland变分原理中泛函的下方有界的要求作了相应的削弱，从而扩大了适用泛函的范围。

The proof primarily makes use of brouwer fixed point theorem and mathematical economicsThe second part of paper discuss the traffic volume change model of freeway.the change rate model on the freeway is key that we establish tollstandard.

证明主要运用的是布劳威尔不动点定理和数理经济学理论。论文第二部分主要是讨论高速公路的交通量转移率模型，高速公路上的实际交通量是我们制定收费标准的关键。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

Double homoclinic loops; Resonant eigenvalues; Nontwist; Periodic orbit; Bifurcation; Periodic solution; Predator-prey system; Fixed point theorem; Coincidence degree; Delay; Functional response function

基础科学，数学，动力系统理论双同宿环；共振特征根；非扭曲；周期轨；分支；周期解；捕食者-食饵系统；不动点定理；重合度；时滞；功能反应函数

Since bounded closed sets in infinite dimensional space are notcompact generally,in order to employ Horn's fixed point theorem the compactness of operator Pis initially proved in section 3 in this chapter.

由于无限维空间的有界闭集一般不具备紧性，为了应用Horn不动点定理，我们先证明了Poincare算子P的紧性。

Does research in a common fixed point theorem of fuzzy mapping s in inequality conditions and the cut set is the nonempty closed bounded subsets of,while is complete metric space.

2，研究了在完备度量空间中一对模糊映象满足一些特定不等式条件，以及当其截集是中非空有界闭集时，该对模糊映象的公共不动点的存在性问题。

In chapter one, by using a competely continuous operator on cone and the Krasnoselskii fixed point theorem, we study the existence of positive periodic solutions of differential equations with impulses and delays, and some sufficient conditions will be given.

第一章讨论了一类具脉冲时滞微分方程周期正解的存在性，通过建立锥上的全连续算子，利用Krasnoselskii不动点定理，得到了存在周期正解的若干充分条件。

By using the theory of linear evolution systems and Sadovskii's fixed point theorem, chapter3 deals with the existence of mid-solutions,strong solutions for the Cauchy problems of neutralabstract functional differential equations dependent on time with unbounded delay, here theright function in the equations satisfies the Caratheodory conditions.

第三章利用线性发展系统理论和Sadovskii不动点定理研究了具有无穷时滞中立型时变泛函微分方程Cauchy问题mild-解、强解的存在性。其中方程的右端函数满足Caratheodory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。