A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces

In this paper, we introduce two iterative schemes by the general iterative method for finding a common element of the set of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Then, we prove two strong convergence theorems for nonexpansive mappings to solve a unique solution of the variational inequality which is the optimality condition for the minimization problem. These results extended and improved the corresponding results of Marino and Xu [G. Marino, H.K. Xu, A general iterative method for nonexpansive mapping in Hilbert spaces, J. Math. Anal. Appl. 318 (2006) 43-52], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (1) (2007) 506-515], and many others.     

EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR NONLINEAR THIRD-ORDER ROBIN BOUNDARY VALUE PROBLEM WITH A TURNING POINT

The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear third- order Robin boundary value problem with a turning point.In order to achieve this aim,existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions.In this manner,the goal of this paper is gained by applying the existence and uniqueness results mentioned above.     

三包层WⅠ和WⅡ型单模光纤波导色散特性的研究

研究了三包层WⅠ和WⅡ型单模光纤的波导色散特性。结果发现在相同条件下，三包层WⅠ和WⅡ型单模光纤零色散点的调节范围比传统的双包层W型单模光纤明显增大。详细分析了几何参量P、Q和光学参量R1、R2对单模传输时的波导色散特性和低次模截止频率的影响。所得的研究结果为获得更为理想的色散补偿、色散平坦光纤及设计新型无源光器件提供了重要的依据。计算波导色散的方法可推广到多包层光纤。     

Separating points of measures on effect algebras

We prove the existence of separating points for every countable family of nonatomic σ-additive modular measures on a σ-complete lattice ordered effect algebra.      

Variational conclusions of set-valued bifunctions on convex subsets of Banach spaces with applications

In this paper, variational conclusions of set-valued bifunctions on convex subsets of Banach spaces are investigated and several new results are obtained. The results are applied to the fixed point theory and variational inequalities. We obtain two fixed point theorems and existence theorems of solutions of variational inequalities.     

高维电报方程的对称周期解

讨论n维电报方程的对称周期解．利用Schauder不动点定理，在非共振条件下给出了一个存在性定理．     

高阶线性微分方程的解及其解的导数的不动点

研究了复域齐次和非齐次线性微分方程的解及其解的导数的不动点与超级问题,得到了整函数系数的齐次和非齐次线性微分方程的解及其解的导数的不动点的两个结果,所得结果推广了一些相关结果.     

Existence for bounded positive solutions of Schrödinger equations in two-dimensional exterior domains

In this paper, by using the fixed point theory, under quite general conditions on the nonlinear term, we obtain an existence result of bounded positive solutions of Schrödinger equations in two-dimensional exterior domains.     

On the limit cycles of a quintic planar vector field

This paper concerns the number and distributions of limit cycles in a Z_2-equivariant quintic planar vector field.25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation.It can be concluded that H(5)≥25=5~2, where H(5)is the Hilbert number for quintic polynomial systems.The results obtained are useful to study the weakened 16th Hilbert problem.     

套代数子空间的端点

设d为套代数AlgN的子空间且包含AlgN的所有一秩算子．利用预零化子d⊥中一秩算子,我们给出了单位球d1中端点的刻画．