常维的p-Laplacian系统的周期解

通过临界点理论中的鞍点定理和极小化作用原理证明了具有非自治的p次线性的常维的p-Laplacian系统的周期解的存在性.

Abstract：

The existence of periodic solutions is studied for ordinary p-Laplacian systems involving non-autonomous p-sublinear by using the saddle point theorem and the least action principle in critical point theory.     

线性空间中集值映射向量优化问题的ε-真有效解

利用一种称为代数型闭包的向量闭包,讨论了线性空间中极值映射向量优化问题的ε-真有效解,在集值映射为广义向量似凸的假设下,建立了这种解的标量化定理和ε-Lagrange乘子定理.

Abstract：

The authors use a concept of algebraic type of closure which is called vector closure . Through this closure they discuss ε-properly efficient solutions of vector optimization problems with set-valued maps. Under the assumption of the generalized cone-subconvexlikeness for Set-valued maps, the authors obtain the scalarization theorem and the ε-Lagrange multipliers theorems for ε-properly efficient solutions of vector optimization problems with set-valued maps.     

关于三个问题的混合粘性迭代

在Hilbert空间中,对求解混合平衡问题、非扩张映射不动点问题及单调L-Lipschitz连续映射变分不等式问题解的公共元,引入了由粘性迭代方法确定的迭代序列.在一些参数控制条件下获得了一个强收敛定理.

Abstract：

This paper introduces an iterative sequence for finding a common element of the set of solutions of a mixed equilibrium problem,the set of fixed point problem of nonexpansive mapping and the set of solutions of the variational inequality problem.A strong convergence theorem is obtained under some parameter controlling conditions.     

一类非线性系统的高增益输出反馈控制

对一类具有非稳定化的线性部分和未知扰动非线性系统进行高增益输出反馈控制设计.首先通过一个线性状态变换,将原系统变为一个线性部分可稳定化的新系统;其次,对观测器和控制器进行设计.控制器保证了闭环系统平衡态的全局渐进稳定.

Abstract：

A high-gain observer control design is considered for a class of nonlinear systems with unstabilizable linear part and unknown disturbances,By a linear state transformation,the original system is transformed into a system with stabilizable linear part.A controller accompanied by an observer is constructed.The controller guarantees the globally asymptotic stability of the origin of the closed-loop system.     

一类非线性非单调二元算子方程组的解

利用锥理论和单调迭代技巧,得到了一类非线性非单调二元算子方程组的解的存在唯一性、迭代逼近序列及误差估计式.

Abstract：

By using the cone theory and monotone iterative technique, the existence and uniqueness of the solutions for a kind of nonlinear non-monotone systems of two binary operator equations, and their conver-gent iterative sequence and error estimations are obtained.     

一类中立型微分方程周期解的存在性与唯一性

利用Krasnoselskii不动点理论,结合分析的方法,对一类中立型微分方程存在周期解进行定性与定量研究,获得了这类微分方程周期解存在性与唯一性的充分条件.

Abstract：

Using the analytical method and utilizing Krasnoselskii's fixed point theory, this paper qualitatively and quantitatively study the existence of the periodic solutions for a class of neutral differential equation, and obtains some sufficient conditions of existence and uniqueness of periodic solutions for this class equations.     

一类新的含A-单调映像的完全广义集值强非线性混合隐拟变分包含

在Hilbert空间中引入和研究了一类新的包含A-单调映像的完全广义集值强非线性混合隐拟变分包含.通过应用A-单调映像的预解算子技巧,构造了一个新的迭代算法来逼近此类变分包含的解.讨论了由此算法产生的迭代序列的收敛分析.

Abstract：

A new class of completely generalized set-valued strongly nonlinear mixed implicit quasi-variational inclusions involving A-monotone mapping is introduced and investigated in Hilbert spaces. A new iterative algorithm for approximating the solutions of this class of completely generalized set-valued strong nonlinear mixed implict quasivariational inclusions is constructed by applying resolvent operator technique for A-monotone mapp1ng. The convergence analysis of the iterative sequences generated by the algorithm is discussed.     

Broer-Kaup系统的达布变换及其偶孤子解

借助谱问题的规范变换,给出Broer-Kaup系统的达布变换,利用达布变换来产生Broer-Kaup系统的偶孤子解,并且用行列式的形式来表达Broer-Kaup系统的偶孤子解.作为应用,Broer-Kaup系统偶孤子解的前两个例子被给出.

Abstract：

A new Darboux transformation associated with the Broer-Kaup system is derived with the help of a gauge transformation of spectral problems. By using Darboux transformation, even-soliton solutions of the Broer-Kaup system are obtained and presented in a determinant form. As an application, the first two cases are given.     

一类五阶非线性演化方程的广义孤立波解和周期解

应用指数函数法,借助计算机代数系统获得了包括五阶KdV方程、Sawada-Kotera方程和Kaup-Kupershmit方程在内的一类五阶非线性演化方程的广义孤立波解和周期解.结果表明,指数函数法结合符号计算已成为解决数学物理中非线性演化方程的强有力工具.

Abstract：

In this paper,the exp-function method is used to obtain generalized solitary wave solutions and periodic solutions for a class of fifth-order nonlinear evolution equations,which include different forms of fifth-order KdV equations,Sawada-Kotera equations and Kaup-Kupershmit equations.The results show that the exp-function method,with the help of symbolic computation,provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.