1) Cone Fixed Point
锥不动点
1.
Mainly by means of the Hopf bifurcation theorem and the cone fixed point theorem in the functional differential equations.
本文对非线性项为两种形式的时滞Van der Pol方程分别加以比较,利用Hopf分支理论和锥不动点定理,得到相应方程在周期解和Hopf分支方面上的差异。
2.
The ordinary differential Van der Pol equation and the functional differential Van der Pol equation with delays whose nonlinear terms are in two different forms are compared accordingly in this paper,mainly by means of the planar qualitative theory,the Hopf bifurcation theorem and the cone fixed point theorem in the functional differential equations.
本文对非线性项为两种形式的常微Van der Pol方程和时滞Van der Pol方程分别加以比较，主要利用平面定性理论、Hopf分支理论和锥不动点定理，得到相应方程在周期解和Hopf分支方面上的差异，从而一定程度上体现了常微分方程和泛函微分方程在具体方程上的差异。
2) fixed point theorem in cones
锥不动点定理
1.
It is proved that such a problem has at least two nonnegative T-periodic solutions by using fixed point theorem in cones under our reasonable conditions.
并利用锥不动点定理证明了在适当的条件下这个问题至少存在两个解。
2.
Existence is established using a fixed point theorem in cones.
研究了Logistic差分方程单个和多重周期正解的存在性理论,利用锥不动点定理证明了解的存在性,并应用本文的理论验证了一些生物数学模型。
3.
The existence of the first solution is obtained by using a nonlinear alternative of Leray-Schauder,and the second one is found by using a Krasnoselskii fixed point theorem in cones.
第一个正解的存在性是利用非线性L eray-Schauder抉择定理得到的,第二个解是利用K rasnoselsk ii锥不动点定理得到的。
3) fixed point theorem
锥不动点定理
1.
Some sufficient conditions for the existence and multiplicity solutions of positive periodic solutions were obtained by using the fixed point theorem.
讨论一类具分布时滞的微分方程正周期解问题,利用锥不动点定理,获得了这类问题正解存在性和多重性的充分条件,推广和改进了已有文献的相关结果。
2.
In this paper,we discuss the existence of positive solution for singular positive boundary value problem of second order differential equations by using a general cone fixed point theorem.
利用一个普通的锥不动点定理研究了二阶奇异非共振边值问题正解的存在性。
3.
Employing a fixed point theorem in cones,we discussed mainly the existence of positive solution to periodic problems for the first impulsive functional differential equations,obtained the existence positive periodic solutions of the problem for first impulsive functional differential equations with delay.
利用锥不动点定理研究有脉冲的一阶泛函微分方程正周期解的存在性,给出了多时滞的一阶脉冲微分方程周期解存在的充分条件,并且讨论了生态学中所提出的几类时滞脉冲微分方程模型,包括红细胞再生模型、果蝇模型和多时滞的Logistic方程等。
4) fixed point index in cones
锥不动点指数
1.
We discuss the existence of non-negative solutions to the fourth-order nonlinear ordinary differential equations two-point boundary value problem,and obtain sufficient conditions of the non-negative existence by using the theory of fixed point index in cones.
利用锥不动点指数理论得到了方程存在非负解的充分条件。
5) fixed point theorem in cone
锥不动点定理
1.
we present a new existence theory for muitiple positive solutions to a kind of second-order discrete periodic boundary value problems by employing a fixed point theorem in cones.
运用锥不动点定理,给出了一种二阶离散周期边值问题多重正解的新的存在性定理。
2.
This paper presents a new existence theory for positive solutions to a kind of second-order discrete periodic boundary value problems by employing a fixed point theorem in cones.
运用锥不动点定理,给出了二阶离散周期边值问题正解的新的存在性定理。
6) fixed point theorem of cone
锥上不动点定理
1.
Using the fixed point theorem of cone expansion and compression of norm type, the existence of multiple C1 [0, 1] positive solutions are given to singular three-point boundary value problems of a class of second order differential equations whereη∈(0, 1) is a constant,λ1∈(0, 1),λ2∈(1,∞),α∈C((0, 1), [0,∞)).
应用锥上不动点定理,给出了二阶三点奇异边值问题至少有两个C1[0,1]正解的存在性。
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