2) coupled fixed point theorems
耦合不动点定理
1.
Our analysis rely on a coupled system of nonlinear fractional differential equations and coupled fixed point theorems.
首先应用耦合不动点定理及耦合的下、上拟解方法证明非线性分数阶微分方程系统正耦合拟解的存在性,然后应用耦合不动点定理证明其正解的唯一性。
3) fixed point theorem of condensing mapping
凝聚映射的不动点定理
1.
Based on the partial order theory, Kuratowski measure of noncompactness, fixed point theorem of condensing mapping and the fixed point index theory in cones, the paper discussed the existence of solutions to the Sturm-Liouville problemsin Banach spaces and the main results are as follows:1.
本文利用半序理论，非紧性测度，凝聚映射的不动点定理及锥上的不动点指数理论，讨论了Banach空间E中Sturm-Liouville边值问题 -(p(t)u′(t))′+q(t)u(t)=f(t，u(t))，t∈[0，1] α_0u(0)-β_0p(0)u′(0)=θ，α_1u(1)+β_1p(1)u′(1)=θ，解的存在性，主要结果有： 一、通过建立新的极大值原理，讨论Banach空间中一般的Sturm-Liouville问题解的存在性，在不假定f(t，u)连续，仅假定f(t，u)满足弱Caratheodory条件，运用上下解单调迭代方法，并结合非紧性测度的性质，研究了Sturm-Liouville边值问题最大解与最小解的存在性。
4) fixed-point theorem
不动点定理
1.
By using fixed-point theorem in cones and fixed-point index theory,a class of discrete P-Laplacian boundary value problem was discussed and a sufficient condition of existence of one or two positive solutions was obtained.
利用锥上的不动点定理及不动点指标理论对一类离散P-Laplacian边值问题正解的存在性进行了讨论,得到了该问题存在一个及两个正解的充分条件。
2.
This paper presents an algorithm based on fixed-point theorem and Quine.
论文提出了一种基于不动点定理和Quine的建立自修复式程序的算法。
3.
By means of Darbo s fixed-point theorem,an existence result of solution for two-point boundary value problem of nonlinear fractional differential equation is obtained.
讨论了非线性分数阶微分方程的两点边值问题,其中的导数是Caputo型分数阶导数,非线性项是Carathéodory函数,应用Darbo不动点定理,证明其在L(0,1)中存在解。
5) fixed point theorems
不动点定理
1.
Common fixed point theorems for Altman type mappings;
Altman型映射的公共不动点定理
2.
With the help of Maximum principle,Picard existence and uniqueness theorem and LeraySchauder fixed point theorems,the existence and uniqueness of the solution of nonlinear coupled differentio-integral system whose geometrical model is area-preserving curvature flow on the plane are proved.
利用最大值定理、Picard存在惟一性定理和Leray Schauder不动点定理,证明了一个几何模型为平面保面积曲率流的非线性耦合微分-积分方程组的解的存在惟一性。
3.
Using the fixed point theorems of cone mapping,a method is given to decide the existence of positive solution of second order two points boundary value problem with sign change of nonlinearities.
利用上下解方法,构造相应锥映射,运用锥映射不动点定理,给出非线性项变号的二阶两点边值问题正解存在性的判定方法,推广了已有文献中相应的结果。
6) the fixed point theorem
不动点定理
1.
In this paper, an existence and uniqueness theorem of positive solutions to a class of semilinear ellipic equations is proved by using the fixed point theorem in Banach space.
该文主要采用 Banack空间中的不动点定理 ,研究了一类半线性椭圆型方程正解的存在性与唯一性 ,并且获得这类椭圆型方程正解存在的一个必要条件。
2.
An existence of positive solution to the semilinear elliptic equation system is proved by using the fixed point theorem.
以不动点定理为主要工具，证明了一类半线性椭圆型方程组正解的存在性，并通过对非线性项适当的限制，给出了唯一性的证
3.
A class of nonlinear n-order boundary value problems was studied and the existence of non-trivial positive solution was obtained by making use of the fixed point theorem in cone,on the basis of which we have estabished several sufficient conditions for the existence of non-trivial positive solution to the nonlinear n-order boundary value problem and improved the results published in literatures.
利用不动点定理和积分方程研究了一类非线性n-阶边值问题,获得了其非平凡正解存在性的新结果。
补充资料：Borel不动点定理
Borel不动点定理
Borel fixed - point theorem
B吮l不动点定理{B.限l五xe小州nt价e僻m二匆卿，T侧邓吧，f.01”聊叉B“狱班滋n卜.王j 设F为代数闭域kl二非空完全代数簇，正则地作用于犷上的连通可解代数群G(见变换的代数群扭1罗-braic goup of transformat一ons))在卜中有不动点.由这个定理可以推出代数群的B.耽l子群(Borel sub-grouP)是共扼的(Bore卜MOI洲)叉)B定理(Borel一Moro-zov theorem))，不动点定理是A.Borel([lj)证明的.Borel定理可以推广到任意域k(不一定代数封闭卜设F为在域k上定义的完全簇若连通可解k分裂群(人一sPlit grouP)G正则地作用在F上，则有理人点集V(k)或者为空集，或者它包含G的一个不动点.因此推广的Bore]子群共扼性定理是:若域k是完满的，则一个连通人定义的代数群H的极大连通可解北可裂子群，在H的k点构成的群中元素作用下互相共辘(f21)，
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参考词条