Existence of multiple fixed points for nonlinear operators and applications

In this paper, by the fixed point index theory, the number of fixed points for sublinear and asymptotically linear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least nine or seven distinct fixed points for sublinear and asymptotically linear operators is proved. Finally, the theoretical results are applied to a nonlinear system of Hammerstein integral equations.     

新型MIp~+-Al_(0.3)Ga_(0.7)As/p-n-n~+-GaAs太阳电池的设计与I-V特性理论分析

为充分利用太阳光的短波部分,将AlxGa1-xAs设计为电池的又一个光伏工作层,并引入固定负电荷,建立界面感应势垒,形成MIp -AlGaAs感应结,有效降低界面对光生电子的复合。以制作工艺简单的p -AlGaAs／p-GaAs界面,将感应结与p／n-GaAs部分连接起来,构成新型高效率复合结构MIp -Al0.3Ga0.7As／p-n-n -GaAs太阳电池。其I-V特性理论研究绐果表明,选择合适的负电荷面密度数和Al0.3Ga0.7As层的掺杂浓度,即:建立合适高度的感应势垒,可显著降低界面复合速度近8个数量级。优化设计得到的整个电池的效率为31.5％,较传统的窗口层电池有明显提高。     

Common fixed point results for noncommuting mappings without continuity in cone metric spaces

The existence of coincidence points and common fixed points for mappings satisfying certain contractive conditions, without appealing to continuity, in a cone metric space is established. These results generalize several well-known comparable results in the literature.     

关于伪压缩映象不动点迭代的一点注记

设$K$是自反的并且具有一致Gateaux可微范数的Banach空间$E$的非空有界闭凸子集.设$T:K\rightarrow K$是一致连续的伪压缩映象.假设$K$的每一非空有界闭凸子集对非扩张映象具有不动点性质.设$\{\lambda_n\}$是$(0,\frac{1}{2}]$中序列满足: (i) $\lim_{n\rightarrow \infty}\lambda_n=0$; (ii) $\sum_{n=0}^{\infty}\lambda_n=\infty$.任给$x_1\in K$,定义迭代序列$\{x_n\}$为:$x_{n+1}=(1-\lambda_n)x_n+\lambda_nTx_n-\lambda_n(x_n-x_1),n\geq 1.$若$\lim_{n\rightarrow \infty}\|x_n-Tx_n\|=0$, 则上述迭代产生的$\{x_n\}$强收敛到$T$的不动点.     

渐近φ伪压缩映象有限族的迭代程序的强收敛(英文)

Strong convergence theorems for approximation of common fixed points of asymptoticallyφ-quasi-pseudocontractive mappings and asymptoticallyφ-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new compos- ite implicit iteration scheme with errors.The results presented in this paper extend and improve the main results of Sun,Gu and Osilike published on J.Math.Anal. Appl.     

二阶共振周期边值问题多解的存在性

借助于与给定共振的非线性周期边值问题相关的非共振的线性边值问题来构造算子,利用范数形式的锥拉伸-压缩不动点定理,得到了非线性周期边值问题非负解的存在性定理.     

Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.     

MULTIPLE POSITIVE SOLUTIONS TO SOME SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEMS

Multiplicity of positive solutions to some second order m-point boundary value problems are considered. By fixed-point theorems in a cone, some new results are obtained. The associated Green’s function of these problems are also given.     

On a graded mesh method for a class of weakly singular Volterra integral equations

In this paper a class of weakly singular Volterra integral equations with an infinite set of solutions is investigated. Among the set of solutions only one particular solution is smooth and all others are singular at the origin. The numerical solution of this class of equations has been a difficult topic to analyze and has received much previous investigation. The aim of this paper is to improve the convergence rates by a graded mesh method. The convergence rates are proved and a variety of numerical examples are provided to support the theoretical findings.