Existence of sign-changing solutions for the p-Laplacian equation from linking type theorem

In this paper, the existence of sign-changing solutions for p-Laplacian equation is obtained via a new linking theorem.     

Weak convergence theorem for Lipschizian pseudocontraction semigroups in Banach spaces

The purpose of this paper is to study the weak convergence problems of the irnplicity iteration process for Lipschitzian pseudocontraction semigroups in general Banach spaces. The results presented in this paper extend and improve the corresponding results of Zhou [Nonlinear Anal., 68, 2977-2983 （2008）], Chen, et ah [J. Math. Anal. Appl., 314, 701 709 （2006）], Xu and Ori [Numer. Funct. Anal. Optim, 22, 767-773 （2001）] and Osilike [J. Math. Anal. Appl., 294, 73-81 （2004）]. Keywords     

A generalized existence theorem of backward doubly stochastic differential equations

In this paper, we deal with a class of one-dimensional backward doubly stochastic differential equations （BDSDEs）. We obtain a generalized comparison theorem and a generalized existence theorem of BDSDEs.     

A remark about the Orlicz-Pettis theorem and the statistical convergence

In this paper we obtain a new version of the Orlicz-Pettis theorem by using statistical convergence. To obtain this result we prove a theorem of uniform convergence on matrices related to the statistical convergence.     

Convergence theorems for λ-strict pseudo-contractions in q-uniformly smooth Banach spaces

In this paper, we continue to discuss the properties of iterates generated by a strict pseudo- contraction or a finite family of strict pseudo-contractions in a real q-uniformly smooth Banach space. The results presented in this paper are interesting extensions and improvements upon those known ones of Marino and Xu [Marino, G., Xu, H. K.： Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl., 324, 336-349 （2007）]. In order to get a strong convergence theorem, we modify the normal Mann＇s iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in C. This result extends a recent result of Kim and Xu [Kim, T. H., Xu, H. K.： Strong convergence of modified Mann iterations. Nonl. Anal., 61, 51- 60 （2005）] both from nonexpansive mappings to λ-strict pseudo-contractions and from Hilbert spaces to q-uniformly smooth Banach spaces.     

关于曲线积分中值定理“中间点”渐近性的进一步结果

给出一个曲线积分学中值定理及其"中间点"渐近性分析,其结果还概括了近五年来关于积分学第一中值定理"中间点"渐近性的众多结果.     

应用留数定理计算一类实积分

应用留数定理,通过构造被积函数,将一类实积分的计算问题转化为求留数的计算,得到求此类问题的一种解法.     

一维紧邻时间随机环境下可逗留随机游动的有关性质

给出了可数状态空间中时间随机环境下可逗留随机游动的一个统一模型,对于一维紧邻时间随机环境下的随机游动,在一定的条件下,讨论它的极限性质和中心极限定理,该结论类似于空间随机环境下的随机游动的有关结论.     

直线与圆的定理及空间推广的应用

在教学“直线与圆的位置关系”（记为【定理一】）时,受文（1）的启发,笔者首先发现了【定理一】的空间推广（记为【定理二】）,向学生们进行了介绍,取得了很好的教学效果．又想：能否用【定理一】和【定理二】来简洁地解决一些数学问题呢？经探究,欣喜地发现：答案是肯定的．     

sl(2,F)PBW定理的另一种证明

设F是任意域,L是F上任意一个李代数,文献[1]给出了关于L的PBW定理及证明.本文对L=sl(2,F)我们给出了PBW定理的另一种证明方法.