1) degree for condensing map
凝聚映射的度
2) condensing map
凝聚映射
1.
Under the ordered conditions and noncompactness measure conditions,the existence of positive periodic solution for second-order ordinary differential equation in Banach space was proved by accurately calculating the measure of noncompactness and employing fixed-point index theorems of condensing map.
在一定的序条件及非紧性测度条件下,通过非紧性测度的精细计算,运用凝聚映射的不动点指数理论获得有序Banach空间二阶常微分方程的正周期解的存在性。
2.
Under the nonmonotone conditions,the results of existence of periodic boundary value problem of second order ordinary differential equation in Banach space is obtained by employing measure of noncompactness,degree of condensing map and Sadvoskii fixed point theorem.
在Banach空间中,非线性f(t,u)项关于u非单调条件下,讨论了二阶常微分方程周期边值问题解的存在性,所用的工具是非紧性测度,凝聚映射的拓扑度及Sadovskii不动点定理。
3.
The theory of non-compactness measure and Sadovskii fixed point theorem of condensing map are applied to these problems,and some existence results are obtained.
研究了Banach空间中二阶Neumann边值问题解的存在性,利用非紧性测度的性质和凝聚映射的Sadovskii不动点定理,获得了若干解的存在性定理。
3) condensing mapping
凝聚映射
1.
We study the solvability of 0∈(R(T+C)) making use of condensing mappings′degree theorey.
分别在C(T+I-)1非扩张与C(λT+I)-1紧的情况下,利用凝聚映射的度理论,考虑了方程0∈R(T+C)的可解性问题。
2.
Under an order condition of nonlinear term which could be easily verified, the existence of positive solutions is proved by the topological degree theory of condensing mapping.
讨论了有序Banach空间中的非线性二阶Dirichlet边值问题正解的存在性,并在非线性项满足一个易检验的序条件下,应用凝聚映射的拓扑度理论获得了该问题正解的存在性结果。
3.
Under more general conditions,an existence result of positive solutions was obtained by employing a new estimate of noncompactness measure and the fixed point index theory of condensing mapping.
在较一般的条件下用新的非紧性测度的估计技巧与凝聚映射的不动点指数理论获得了该问题正解的存在性结果。
4) condensive mapping
凝聚映射
1.
The corresponding results on condensive mapping are discussed in section 3.
其中第二节中考虑了算子的奇性 ,运用 Borsuk定理得出了 m-增生、奇算子的映射定理 ;在第三节中讨论了凝聚映射的相应结
5) degree for α condensing maps
凝聚映象的度
6) Ψ*-condensing map
Ψ*-凝聚映射
1.
The definition of Ψ*Ψ*-condensing map on generalized convex spaces was introduced,and its some properties and fixed point theorems were given,finally existence problems of maximal element and existence problem of equilibrium point in abstract economy system were discussed as their applications.
介绍了一般化凸空间上的Ψ*-凝聚映射的定义,并给出了它的一些性质和不动点定理,最后作为它们的应用,讨论了极大元存在问题和在抽象经济系统中的平衡点的存在问题。
补充资料：映射度
映射度
degree of a mapping
映射度呻犯概ofa“.功卿啥;eTeue。‘or浦脚以eH。:] 两个相同维数紧连通流形之间的连续映射(con-tinUOus Ir.PPing)f:(M，刁M)~(N，日N)的度(de-g代)是一个整数degf，使得f.(拜M)=degf·拼N，其中召M，拜N分别为流形M与N的基本类(几m血~-tald理洛)，关于系数环z或Z:而取的，而f.为诱导映射.对于不可定向流形，映射度模2唯一确定.若f:M~N为两个闭微分流形之间的可微映射，则模2的由gf即等于f的任一正则值y的逆象集的点数.在可定向流形的情形下， 吨f=艺s咖Jx， 二。f一1(夕)其中s堪”Jx为f在点x的Jaco饭行列式的正负号(Bro~咚射李(Bro~Inapping degree)). 对于连续映射f:(R”，O)~(R”，0)以及f一‘中的孤立点x，可以定义点x处的局部映射度(b。红Tnapp吨d哪，无)吨二f:deg二f=deg二h，其中h是f在小球面 S:=刁B:，B署自f一’(o)，x任Int丑健上的限制，二为从0点向单位球面的射影.对于可微映射f则有公式 }d电二fl=d面Q(f)一Zd而I，其中Q(f)为在0处光滑函数芽(罗m)所构成的环关于f的分量所生成理想的商环，I为商环关于性质尸二O的最大理想.令几“Q(f)表示映射f的Jacobi行列式所代表的等价类，则对于满足价(J。)>O的线性型似Q(f)~R，公式degxf=Index<，>，成立，其中
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