1) fixed point index theorem
不动点指标定理
1.
By using a well-known fixed point index theorem,we obtain the existence,multiplicity and nonexistence of positive periodic solution(s) to this equation.
利用一个著名的不动点指标定理,获得了该方程周期正解的存在性、多重性和不存在性。
2) fixed point index theorem
不动点指数定理
1.
This paper establishes the existence of multiple positive solutions of a class of nonlinear three-point boundary value problems by means of the fixed point index theorem on cones.
利用锥映射的不动点指数定理,建立了一类三点边值问题多个正解的存在性定理。
2.
This paper establishes the existence of multiple positive solutions of a class of singular nonlinear three-point boundary value problems by means of the fixed point index theorem on cones.
利用锥映射的不动点指数定理,建立了一类奇异三点边值问题多个正解的存在性定理。
3) fixed points index
不动点指标
1.
By means of the spectral properties of positive compact linear differential operators and fixed points index of compact maps in cones, combining with maximum principles, lowerupper solutions methods, sufficient conditions of positive solutions for a cooperative system with saturation are obtained.
利用正的紧线性微分算子的谱性质和锥映象不动点指标,结合极值原理,上下解方法,得到了具有饱和项的互惠模型正解存在的充分条件。
2.
This paper studies the steady-state equation of a kind of predator-prey model,and by using the spectral properties of positive compact linear differential opetators and fixed points index of compact maps in cones,combining with maximum principles,and lower-upper solutions methods,sufficient conditions of positive solutions are obtained.
研究了一类捕食模型的平衡态方程,通过利用正的紧线性微分算子的谱性质和锥映像不动点指标,结合极值原理,上下解方法,得到了正解存在的充分条件。
3.
By using the spectral properties of positive compact linear differential opetators and fixed points index of compact maps in cones,combining with maximum principles and lower-upper solutions method,the steady-state equation of a kind of the Volterra-Lotka cooperative model with saturation is studied,sufficient conditions for the existence of positive solutions of the system are obtained.
利用正的紧线性微分算子的谱性质和锥映象不动点指标,结合极值原理和上下解方法,研究了具有饱和项的Volterra-Lotka互惠模型的平衡态方程,得到了具有饱和项的互惠模型正解存在的充分条件。
4) fixed point index
不动点指标
1.
Using the fixed point index theory,the indices of the trival and semi-trival solutions are computed.
在此基础上 ,用不动点指标理论计算了平凡解和半平凡解的不动点指标 ,从而得到当平凡解和半平凡解的不动点指标之和不等于 1时其共生态的存在
2.
By means of fixed point index of compact maps in cones, combining with maximum principles and lower-upper solution methods, sufficient conditions for coexistence are obtained.
利用Leray-Schauder度理论,通过计算锥映射不动点指标,结合极值原理、上下解方法,得到了正解存在的充分条件。
5) fixed-point index theorem
锥上不动点指数定理
6) Krasnoselskii fixed-point index theorem
Krasnoselskii不动点指数定理
1.
By using Krasnoselskii fixed-point index theorem, a class of nonlinear functional differential equation x′(t)=a(t)g(x(t))x(t)-λ sum from i=1 to n(f_i(t,x(t-T_i(t)))) is obtained,and at least there are the sufficient conditions to guarantee the existence of two periodic positive solutions, and some corresponding results in existing literatures are expanded.
利用Krasnoselskii不动点指数定理,得到一类带有参数的非线性泛函微分方程x′(t)=a(t)g(x(t))x(t)-λ sum from i=1 to n(f_i(t,x(t-T_i(t)))),至少存在两个周期正解的充分条件,推广了已有文献中的相关结果。
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