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1.
一类非线性拟变分不等式及其应用   总被引:1,自引:1,他引:0  
本义研究了如下变分不等式问题:求u∈M使得a(u,v-u)+〈Gu,v-u〉≥(f,v-u),(?)u∈M.并将所得结论应用于二阶半线性椭圆型边值问题的求解.  相似文献   

2.
向量值Musielak-Orlicz空间的两种几何性质(英)   总被引:1,自引:0,他引:1  
设X是复Banch空间,M(t,u)是以t为参数的满足某些通常条件的Φ-函数.我们证明了;(i)Musielak-Orlicz空间L_M(X)具有解析UMD性质当且仅当X具有;(ii) L_M(X)具有解析RN性质当且仅当X具有.  相似文献   

3.
设R和T是Noether完备半局部环,R→T是环同态.本文证明了,若T是有限生成或ArtinR-模,M为G-Matlis自反R-模,则对所有n≥0,Ext(T,M),Ext(M,T),Tor(T,M)以及Tor(M,T)均是G-Matlis自反T-模.所得结果推广了R.Belshof的结果.  相似文献   

4.
设M ̄+、M ̄-为单边Hardy-Littlewood极大算子,u(x)、v(x)为实直线R上两个权函数。本文得到M ̄+(或M ̄-)关于测度v(x)dx和u(x)dx是弱(1.1)型的当且仅当(u,v)∈或(u,v).  相似文献   

5.
对文献[1-3]中的结果:ut=div(|u|p-2u)在ΩT=Ω×(0,T)上弱解的空间梯度是Ho¨lder连续的做一个补充.在这个注记里,讨论了条件p>max{1,2NN+2}是怎样由u的性质所决定的.属于LNloc(ΩT)空间解的梯度是Ho¨lder连续的条件仅仅是p>1.  相似文献   

6.
李登峰 《数学杂志》1995,15(4):409-414
设M^+、M^-为单边Hardy-Littlewood极大算子,u(x)、v(x)为实直线R上两相权函数。本文得到M^+(或M^-)关于测度v(x)dx和u(x)dx是弱(1.1)型的当且仅当(u,v)∈A1^+(或(u,v)∈A1^-)。  相似文献   

7.
给出赋Orlicz范数的Musielak-Orlicz序列空间中上(下)单调点以及上(下)局部一致单调点的充分必要条件.  相似文献   

8.
本文给出了赋Orlicz范数的Musielak-Orlicz序列空间的局部一致凸性,(H)性质,(S)性质的判据.  相似文献   

9.
本文主要讨论高维空间非线性波动方程的Cauchy问题整体解的非存在性,我们证明对Uu-△u=f(u),f(u)=c|u|p-1u,当1<p≥时,若初始能量非正,则无论初值数据的ck-范数(连续空间范数)多么小,解按Ck-范数或按Hs(Rn)(S≥1)都在有限时间内Blowup,并且有相同的生命跨度.  相似文献   

10.
给出赋Orlicz范数的Musielak-Orlicz函数空间中光滑点、光滑性、强(很)光滑点和强(很)光滑性的充 分必要条件.  相似文献   

11.
《Quaestiones Mathematicae》2013,36(4):299-313
ABSTRACT

Let Λ be a scalar sequence space which is endowed with a normal locally convex topology. For a separated locally convex space E we denote by Λ(E) the vector space of all sequences g in E for which (>g(i),a<) ε Λ for all a ε E'. We define a locally convex topology ζ on Λ(E) and then characterize the dual of the ζ-closure (denoted by Λc (E)) of the finite sequences in Λ(E). We demonstrate the existence of a continuous projection from Λ(E)' onto a subspace of Λ(E)' which is isomorphic to Λc(E)'. Furthermore, we find a topological decomposition of Λα c (E)”, where one of the factors is isomorphic to Λ;α(E). These results are then applied to find necessary and sufficient conditions for Λα(E) to be semi-reflexive. A parallel development yields the same results for the space Λ(E') of all sequences f in E' for which (>x, f(i)<) ε Λ; for all x ε E, when E is barrelled. We conclude the paper by application of the results on vector sequence spaces to spaces of operators—including for instance, necessary and sufficient conditions for Lb (E,Λ;) and Lb (Λ,E) to be semi-reflexive.  相似文献   

12.
在qw*拓扑的基础上定义了Q空间和Qr空间,重点给出了在拟桶偶对条件下的Qr空间的有界算子的闭图像定理以及描述Qr空间几何特征的重要结论.  相似文献   

13.
In generalising a closed graph theorem of Dektjarev [5] we show that each almost closed and uniformly almost continuous relation of a quasi-uniform space to a hypercomplete quasi-uniform space is uniformly continuous. The hypothesis of being almost closed is necessary and actually weaker than the requirement that the relation considered has a closed graph. Since each topological space can be quasi-uniformized, one obtains closed graph theorems for topological spaces.As consequences we get an analogous closed graph theorem for locally uniformly almost continuous relations and a theorem concerning the completeness of the range of each continuous uniformly almost open mapping of a hypercomplete space to a uniform space.Finally we prove a closed graph theorem for relations to locally compact spaces without referring to any quasi-uniformization and thus without assumptions and statements concerning uniformity.  相似文献   

14.
Densely Continuous Forms in Vietoris Hyperspaces   总被引:2,自引:0,他引:2  
For countably paracompact normal spaces X and locally compact separable metric spaces Y, a characterization is given for the closure of the set of densely continuous forms from X to Y in the hyperspace of nonempty closed subsets of X × Y under the Vietoris topology. This shows that for such X having no isolated points, every closed subset of X × R that is dense over X can be Vietoris approximated by a semicontinuous function on X.  相似文献   

15.
In this paper, we study the well-posedness of the third-order differential equation with finite delay(P_3): αu'"(t) + u"(t) = Au(t) + Bu'(t) + Fut +f(t)(t ∈ T := [0,2π]) with periodic boundary conditions u(0) = u(2π), u'(0) = u"(2π),u"(0)=u"(2π) in periodic Lebesgue-Bochner spaces Lp(T;X) and periodic Besov spaces B_(p,q)~s(T;X), where A and B are closed linear operators on a Banach space X satisfying D(A) ∩ D(B) ≠ {0}, α≠ 0 is a fixed constant and F is a bounded linear operator from Lp([-2π, 0]; X)(resp. Bp,qs([-2π, 0]; X)) into X, ut is given by ut(s) = u(t + s) when s ∈ [-2π,0]. Necessary and sufficient conditions for the Lp-well-posedness(resp. B_(p,q)~s-well-posedness)of(P_3) are given in the above two function spaces. We also give concrete examples that our abstract results may be applied.  相似文献   

16.
For all linear and many nonlinear operators between Fréchet spaces, several continuity results are established. Especially, a new closed graph theorem is given.  相似文献   

17.
In this paper, we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness. Moreover, we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on the behavior of essential spectra of such closed densely defined linear operators on Banach spaces. These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces.  相似文献   

18.
First, we consider a strongly continuous semigroup of nonexpansive mappings defined on a closed convex subset of a complete CAT(0) space and prove a convergence of a Mann iteration to a common fixed point of the mappings. This result is motivated by a result of Kirk (2002) and of Suzuki (2002). Second, we obtain a result on limits of subsequences of Mann iterations of multivalued nonexpansive mappings on metric spaces of hyperbolic type, which leads to a convergence theorem for nonexpansive mappings on these spaces.  相似文献   

19.
We prove a closed graph theorem for Baire locally convex spaces (for Baire linear topological spaces) in the domain and weakly C‐Suslin locally convex spaces (respectively, for C‐Suslin linear topological spaces) in the range which improves some classic closed graph theorems and other, more recent, related results.  相似文献   

20.
This paper contains a detailed study of those locally convex spaces E-which we call GN-spaces-for which the following closed graph theorem holds: Every closed linear map from E to any normed linear space is continuous. In the first two sections we establish some characterisations and permanence-properties of these spaces. The main result reads as follows: Every separated GN-space is isomorphic to a barrelled subspace of some ωd?d′, and conversely. Then we determine those GN-spaces which are (DF)-spaces, Schwartz-spaces or nuclear spaces. Finally we show that neither the strong dual nor the tensor product of GN-spaces are GN-spaces.  相似文献   

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