锥中调和函数的下界及其应用

本文首先给出锥中一类调和函数的下界,所得结果推广了张艳慧、邓冠铁和高洁欣在半空间中的相关结论;作为应用,接着证明了锥中的Levin型定理;最后,给出了锥中Dirichlet问题解积分表示形式的唯一性定理.     

多重次调和函数的一个Phragmén-Lindeloef定理

该文给出了C^N中锥上关于多重次调和函数的一个Phragmé-Lindeloef定理,从而推广了文献[8]的一个结论.     

多重次调和函数的一个 Phragmen-Lindelof定理

文给出了 C^N中锥上关于多重次调和函数的一个 Phragme-Lindelof 定理, 从而推广了文献[8]的一个结论.     

调和函数的Lipschitz型空间和Landau-Bloch型定理

主要研究调和函数和Poisson方程的解的性质.讨论了调和函数的Lipschitz型空间,建立了调和函数的Schwarz-Pick型引理,并利用所得结果证明了与调和Hardy空间有关的一个Landau-Bloch型定理.最后,还利用正规族理论讨论了与Poisson方程的解有关的Landau-Bloch型定理的存在性.     

多重次调和函数的一个Phragmén-Lindel(o)f定理

该文给出了CN中锥上关于多重次调和函数的一个Phragmé-Lindel(o)f定理,从而推广了文献[8]的一个结论.     

无限管状区域上次调和函数的边界性质

作者刻画了定义在无限管状区域中次调和函数的边界性质.通过证明一类新型的Phragm\''{e}n-Lindel\"{o}f定理, 不仅得到了与之相关最大模极限的存在性定理,而且还得到了其具体的表达式.     

集值优化问题超有效解的高阶Mond-Weir对偶

在实赋范线性空间中利用锥方向高阶广义邻接导数研究带约束的集值优化在超有效解意义下的高阶Mond-Weir对偶问题.在广义锥-凸假设下,利用锥方向高阶广义邻接导数的性质借助凸集分离定理得到了强对偶定理.利用超有效点的标量化定理得到逆对偶定理.     

半空间中次调和函数的Phragmn-Lindelf定理及应用

本文利用调和函数的Carleman公式,结合Levi的方法,在半空间中证明了次调和函数的Phragmn-Lindelf定理.作为Phragmn-Lindelf定理的应用,本文引入了半空间中的C类函数,并且得到了次调和函数属于C类函数的一个充分必要条件,从而推广了Ahlfors和Levi等的经典结果.     

用Salagean算子定义的缺系数的单叶调和函数类

本文研究了用Salagean算子定义的缺系数单叶调和函数类.利用从属关系和算子理论得到类中函数的系数估计、极值点、偏差定理、卷积性质、凸性组合与凸半径,推广了已有的一些结果.     

锥内特定调和函数的渐近状态

给出了锥内特定调和函数在无穷远点处的渐近状态,推广了Siegel-Talvila在半空间的相关结果.同时,也得到了锥内Dirichlet问题的解.     

Minimax Problems for Set-Valued Mappings

In this article, by virtue of the Fan-Browder fixed point theorem, we first obtain a minimax theorem and establish an equivalent relationship between the minimax theorem and a cone saddle point theorem for scalar set-valued mappings. Then, by using scalarization functions, we investigate an existence theorem of the cone saddle point for set-valued mappings. Simultaneously, we also establish a minimax theorem for set-valued mappings.     

Local existence of multiple positive solutions to a singular cantilever beam equation

By constructing suitable cone and control functions, we prove some local existence theorems of positive solutions for a singular fourth-order two-point boundary value problem. In mechanics, the problem is called cantilever beam equation. Furthermore, we improve a famous method appeared in the studies of singular boundary value problems. The approximation theorem of completely continuous operators and the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type play important parts in this work.     

Schur-Ostrowski type theorems revisited

In this paper we extend Schur-Ostrowski theorem on Schur-convex functions from majorized vectors to separable ones. For this, we introduce a generalized Schur-Ostrowski?s condition. We apply the obtained result for cone orderings and group-induced cone orderings. Finally, we give some interpretations for absolutely weak majorization and for group majorization on the space of complex matrices.     

锥度量空间中c-距离下的不动点定理

在锥度量空间中,用压缩性函数代替具体实数,获得了c-距离下的映射的新的不动点定理.所得结果在条件上不要求映射的非减性,且第一个定理去掉了锥的正规性,第二个定理去掉了映射的连续性,改进了原有的许多重要结论,并给出了相应的例子.     

General Lagrange multiplier theorems

A cone constraint is used to develop a general Lagrange multiplier theorem for normed linear spaces. Conditions for the payoff functional multiplier to be less than zero are given for Banach spaces. Sufficiency theorems involving Lagrange multipliers are developed for abstract programming problems. Generalizations of certain properties of convex functions will be used for optimization problems.     

Areas and Volumes for Null Cones

Motivated by recent work of Choquet-Bruhat et al. (Class Quantum Gravity 26(135011), 22, 2009), we prove monotonicity properties and comparison results for the area of slices of the null cone of a point in a Lorentzian manifold. We also prove volume comparison results for subsets of the null cone analogous to the Bishop–Gromov relative volume monotonicity theorem and Günther’s volume comparison theorem. We briefly discuss how these estimates may be used to control the null second fundamental form of slices of the null cone in Ricci-flat Lorentzian four-manifolds with null curvature bounded above.     

Banach 空间中分数阶微分方程$m$点边值问题的正解

该文在Banach空间中研究一类分数阶微分方程$m$点边值问题, 证明了格林函数的性质, 构造一个特殊的锥,利用锥拉伸压缩不动点定理得到了该边值问题正解的存在性,最后给出一个例子用以说明主要结果.     

Inequalities for Hardy-type operators on the cone of decreasing functions in a weighted Orlicz space

Modular inequalities and inequalities for the norms of Hardy-type operators on the cone Ω of positive functions and on the cone of positive decreasing functions with common weight and common Young function in a weighted Orlicz space are considered. A reduction theorem for the norm of the Hardy operator on the cone Ω is obtained. It is shown that this norm is equivalent to the norm of a modified operator on the cone of all positive functions in the space under consideration. It is proved that the modified operator is a generalized Hardy-type operator. The equivalence of modular inequalities on the cone Ω and modified modular inequalities on the cone of all positive functions in the Orlicz space is shown. A criterion for the validity of such inequalities in general Orlicz spaces is obtained and refined for weighted Lebesgue spaces.