1) topological degree
拓扑度
1.
The upper and lower solutions of m-point boundary value problems at resonance and topological degree;
m点边值共振问题的上下解和拓扑度
2.
Utilizing laray-schauder topological degree theorems in menger PN space and with the diversification of bounding conditions that the operators should hold,the existence of the solution of nonlinear operator equations Tx=Lx and Tx=Lx+p are studied.
利用概率线性赋范空间中的Leray-Schauder拓扑度理论,通过改变算子所满足的边界条件,研究了非线性算子方程Tx=Lx和Tx-Lx+p的解的存在性问题,在不要求方程满足L≥1的条件下(在文[1,2]中都要求方程满足条件L≥1),得到了几个新的定理。
3.
In this paper,using Brouwer topological degree theory,it is proved that the theorem still holds if we substitute star shape region for convex set.
利用Brouwer拓扑度理论,证明定理中凸性条件进一步减弱为星形区域时,其结论仍然成立。
2) coincidence degree
拓扑度
1.
By using the method of coincidence degree,the existence of positive periodic solution for a discrete time Leslie system with mutual interference was studied.
考虑一类具相互干扰的离散L eslie系统,利用拓扑度方法,获得了该系统正周期解存在的充分条件。
2.
By using Gaines and Mawhin s continuation theorem of coincidence degree theory,a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions to the system.
考虑了一类食饵在斑块环境中扩散具有脉冲和时滞的捕食系统,通过灵活地运用Gaines和Mawhin的连续拓扑度定理,获得了一系列易验证的正周期解存在的充分条件。
3.
A set of easily verifiable sufficient conditions is derived for the global existence of periodic solutions with strictly positive components by using the method of coincidence degree.
通过运用拓扑度方法,获得了该系统至少存在一组可易验证的严格正周期解的充分条件。
3) topology degree
拓扑度
1.
The condition for the existence of positive elliptic periodic solution was found using Floquet theory;and the theorem of the existence of positive elliptic periodic solution was proved by the method of upper and lower solutions and homotopy invariance theory of topology degree;then an example was given.
利用Floquet理论得到了该方程的正椭圆周期解存在的条件;然后利用上下解方法和拓扑度的同伦不变性理论,证明了该模型正椭圆周期解的存在性定理,并进行了实例验证。
2.
Considering the following boundaryprohlem △u+f(x,u,v)=0,△v+g(x,u,v)=0,x∈Ω, B_1(u)=0,B_2(v)=0,where the nonlinear term f is superlinear and g satisfies the conditions of asymptotical linear,by usingthe metheds of the topology degree theory,The paper get some existence results and the case in which theboundary conditions B_1(u)and B_2(v)are different types is also consiuered.
ｆ是超线性的，ｇ是渐近线性的），利用拓扑度理论等工具，得到了几个解的存在性定理。
5) Topological Density
拓扑密度
补充资料：拓扑结构(拓扑)
拓扑结构(拓扑)
topologies 1 structure (topology)
拓扑结构(拓扑)【t哪d哈eal structure(to和如罗);TO-no“orHtlec~cTpyKTypa」，开拓扑(oPen to和fogy)，相应地，闭拓扑(closed topofogy) 集合X的一个子集族必(相应地居)，满足下述J胜质: 1.集合x，以及空集叻，都是族。(相应地容)的元素. 2。(相应地2劝.。中有限个元素的交集(相应地，居中有限个元素的并集)，以及已中任意多个元素的并集(相应地，居中任意多个元素的交集)，都是该族中的元素. 在集合X上引进或定义了拓扑结构(简称拓扑)，该集合就称为拓扑空间(topological sPace)，其夕。素称为.l5(points)，族份(相应地居)中元素称为这个拓扑空问的开(open)(相应地，闭(closed))集. 若X的子集族份或莎之一已经定义，并满足性质l及2。。(或相应地l及2衬，则另一个族可以对偶地定义为第一个集族中元素的补集族. fl .C .A二eKeaH及pos撰[补注1亦见拓扑学(zopolo群);拓扑空l’ed(toPo1O廖-c:，l印aee);一般拓扑学(general toPO】ogy).
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参考词条