Monotonicity and best approximation in Orlicz-Sobolev spaces with the Luxemburg norm

Criteria for strict monotonicity, upper (lower) locally uniform monotonicity and uniform monotonicity of Orlicz-Sobolev spaces with the Luxemburg norm are given. Some applications to best approximation are presented.     

一类次线性算子在非齐型空间上的弱Herz空间中的弱型估计

作者引入了非齐型空间上的弱Herz空间,并建立了一类次线性算子在这些空间中的弱型估计. 作为应用, 证明了由Calder\'on-Zygmund算子和$\os$函数生成的交换子在弱Herz空间中的弱型估计,其中$r\ge1$. 并且Orlicz空间$\os$当$r=1$时即为$\rb$空间;当$r>1$时为$\rb$的子空间.     

齐性空间SU(2n)/Sp(n)的H-同伦指数

令p为大于3的素数.在一定维数限制下,通过把齐性空间SU(2n)/Sp(n)分解为若干个同伦可结合,同伦可交换的H-空间的乘积,进而得到了SU(2n)/Sp(n)的p素H-同伦指数的一个上界.     

Multiple solutions for a nonlinear and non-homogeneous problem in Orlicz-Sobolev spaces

We study a non-homogeneous boundary value problem in a smooth bounded domain in R^N. We prove the existence of at least two non-negative and non-trivial weak solutions. Our approach relies on Orlicz-Sobolev spaces theory combined with adequate variational methods and a variant of Mountain Pass Lemma.     

两点齐性的 Finsler 流形

该文证明任何一个两点齐性的 Finsler 流形一定是黎曼流形. 证明过程中作者将泛函分析中经典的Mazur 定理推广到不一定是绝对齐次的 Minkowski 空间上.     

一类弱奇异边值问题的大范围收敛算法

该文研究如下的弱奇异边值问题: (p(x)y')'=f(x, y),0b₀g(x), 0≤b₀<1, 边值条件为y(0)=A,αy(1)+β y'(1)=γ 或y'(0)=0,αy(1)+βy'(1)=γ (R.K.Pandey 和 Arvind K.Singh 给出了一种求解此问题的二阶有限差分方法^[1]. 在再生核空间中讨论方程解的存在性, 给出一种新的迭代算法,这种迭代算法是大范围收敛的. 给出数值算例并与R. K. Pandey 和Arvind K.Singh 给出的方法进行比较说明该文方法的有效性.     

On the Minimal Solutions of Variational Inequalities in Orlicz-Sobolev Spaces

In this paper, the author studies the existence of the minimal nonnegative solutions of some elliptic variational inequalities in Orlicz-Sobolev spaces on bounded or unbounded domains. She gets some comparison results between different solutions as tools to pass to the limit in the problems and to show the existence of the minimal solutions of the variational inequalities on bounded domains or unbounded domains. In both cases,coercive and noncoercive operators are handled. The sufficient and necessary conditions for the existence of the minimal nonnegative solution of the noncoercive variational inequality on bounded domains are established.     

赋Orlicz范数的Musielak Orlicz序列空间的Gateaux可微点

该文给出赋Orlicz 范数的Musielak Orlicz序列空间中Gateaux可微点（光滑点）与Frechet可微点（强光滑点）的判定准则.在此基础上推出了该空间具有光滑性或强光滑性的充分必要条件.      

Functional inequalities for transient birth-death processes and their applications

We give a new diagram about uniform decay, empty essential spectrum and various functional inequalities, including Poincaré inequalities, super- and weak-Poincaré inequalities, for transient birth-death processes. This diagram is completely opposite to that in ergodic situation, and substantially points out the difference between transient birth-death processes and recurrent ones. The criterion for the empty essential spectrum is achieved. Some matching sufficient and necessary conditions for weak-Poincaré inequalities and super-Poincaré inequalities are also presented.