1) measure of noncompactness
非紧测度
1.
Let γ denote the Kuratowski measure or ball measure of noncompactness.
设Ｇ是具有正则Ｂｏｒｅｌ测度μ的局部紧Ｈａｕｓｄｏｒｆｆ空间，Ｘ是一Ｂａｎａｃｈ空间，γ记非紧测度。
2.
Using a special measure of noncompactness,this paper studies the quadratic integral equationx(t)=h(t)+f(t,x(t)) integral from n=0 to 1k(t,s,x(s))dsand it proves that the equation has a nondecreasing solution x(t)∈C(I).
利用一种特殊的非紧测度,证明二次积分方程x(t)=h(t)+f(t,x(t)) integral from n=0 to 1 k(t,s,x(s))ds t∈I=[0,1]在C(I)上有单调递增的连续解。
3.
By using the method of the fixed point and the measure of noncompactness,the existence of mild solutions without the compactness of semigroup can be got and special cases as f is completely continuous and Lipschitz continuous can also be tackled,which are more extensive and general results.
讨论了Banach空间中非局部条件下半线性微分方程的适度解的存在性,利用不动点和非紧测度的方法,给出了在不需要半群紧性条件下方程适度解的存在性,并且对f是连续紧算子和f是Lipschitz连续的情形做了统一处理,从而得到了更为广泛和一般性的结果。
2) measure of non-compactness
非紧测度
1.
The main tool used is the Kuratowski measure of non-compactness.
所用的主要工具是Kuratowski非紧测度。
3) Kuratowskii α-noncompacted measure
Kuratowskiiα非紧测度
1.
Moreover,operator decomposed technique and Kuratowskii α-noncompacted measure are applied to study the smooth property of the solution.
利用Sobolev插值不等式以及关于时间t的先验估计证明了该方程在无界域上解的存在性;利用算子分解技巧以及Kuratowskiiα非紧测度讨论了解的光滑性;最后得到了该方程在H2(R1)上存在整体吸引子。
4) measure of noncompactness
非紧性测度
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.
In this paper, we get a new fixed point theorem via the measure of noncompactness in locally convex spaces first.
首先利用局部凸空间非紧性测度得到了一个新的不动点定理;接着运用此定理来讨论局部凸空间中Fredholm型非线性积分方程解的存在性,并应用到弱拓扑结构下Fredholm型非线性积分方程解的存在性的讨论。
5) noncompact measure
非紧型测度
6) noncompactness measure
非紧性测度
1.
By using the theory of noncompactness measure and topological degree of condensing map,some existence and uniqueness results of these problems are obtained.
利用非紧性测度的性质与凝聚场拓扑度理论,在一般Banach空间中,获得了二阶周期边值问题解的存在与唯一性结果。
2.
The theory of noncompactness measure and Sadovskii fixed point theorem of condensing map are applied to these problems,and some existence and uniqueness results are obtained.
讨论了一般Banach空间高阶周期边值问题解的存在性,利用非紧性测度与凝聚映射的Sadovskii不动点定理,获得了其解的存在性与唯一性结果。
3.
The theory of noncompactness measure and Sadovskii fixed point theorem of condensing map are applied to study the existence of periodic solution for certain nonlinear evolution equations with noncompact semigroup in Banach space.
利用非紧性测度的性质与凝聚映射的Sadvoskii不动点定理,讨论了Banach空间中具有非紧半群的一类非线性发展方程周期解的存在性。
补充资料：胎紧测度
胎紧测度
tight measure
胎紧测度[咬少t帐asure;n几价。朗M皿pa]【补注】设X是一个拓扑空间，妙(X)是其开集生成的Borel叮域(Borel口一6eld)，‘军(X)是其所有紧集的铺砌(即子集族).省(X)上的一个测度召是胎紧的，如果 拼(B)=sup{拜(K):K三B，K〔才(X)}.X上的一个有限胎紧测度是一个Rad阅.测度(Radonmeasure).如果X是可分的完全度量空间，那么X上每个概率测度都是胎紧的(Ulam胎紧性定理(Ulam石ghtness theorem))，「A2].“胎紧”这一术语是L.此Cam引入的，〔AS]. 更一般地说，设了。、才是集合X上的两个铺砌，刀是定义在了上的一个集函数.如果 s叩{口走A CA八AZ，A氏分}=刀A、一口AZ，那么刀关于才是胎紧的.
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条