一类非线性变分不等式解的稳定性

本研究Ｈｉｌｂｅｒｔ空间中一类强单调非线性变分不等式解的稳定性,所得结果表明强单调非线性变分不等式解的稳定性依赖于对应集合族与映射族的连续性。     

Banach空间中强伪单调变分不等式解的唯一性和稳定性

在自反Banach空间中证明强伪单调变分不等式解的存在唯一性定理.在此基础上研究扰动变分不等式解的稳定性.此外,也在有限维空间中得到了强拟单调变分不等式解的存在性定理.     

无限维Hillbert空间中单调变分不等式解的近似迭代算法

在无穷维Hillbert空间中研究了一类单调型变分不等式，把求单调型变分不等式解的问题转化为求强单调变分不等式的解，建立了一种新的迭代算法，并证明了由算法生成的迭代序列强收敛于单调变分不等式的解，从而推广了所列文献中的许多重要结果．     

广义集值强非线性混合似变分不等式的辅助原理和三步迭代算法

使用辅助原理技巧研究了一类广义集值强非线性混合变分不等式．证明了此类集值强非线性混合变分不等式辅助问题解的存在性和唯一性;构建了一个新的三步迭代算法,通过辅助原理技巧,构建并计算此类非线性混合变分不等式的近似解,进一步证明非线性混合变分不等式解的存在性以及由算法产生的三个序列的收敛性．所得结论推广了近年来许多混合变分不等式和准变分不等式以及他们的有关结果．     

广义集值强非线性混合似变分不等式解的迭代逼近

延拓辅助原理的技巧研究一类取非紧值的集值映象的广义强非线性混合似变分不等式．证明了这类广义强非线性混合似变分不等式的辅助问题解的存在性．利用该存在性结果,给出了解这类广义强非线性混合似变分不等式的迭代算法,最终证明了这类广义强非线性混合似变分不等式解的存在性及由算法生成的迭代序列的收敛性．     

广义集值强非线性混合似变分不等式解的迭代逼近

辅助原理的技巧被延拓来研究一类取非紧值的集值映象的广义强非线性混合似变分不等式.首先,证明了这类广义强非线性混合似变分不等式的辅助问题解的存在性.其次,利用该存在性结果,给出了解这类广义强非线性混合似变分不等式的迭代算法.最后,不仅证明了这类广义强非线性混合似变分不等式解的存在性,而且证明了由算法生成的迭代序列的收敛性.     

一类非线性Signorini问题的有限元逼近

本文讨论了一类与非线性单调算子相联系的变分不等式问题——一类非线性Signorini问题。证明了解的存在性和唯一性,给出解的一个表征性质。随后,构造了问题的一个有限元逼近格式;得到了有限元近似解的收敛性结果和误差估计,关键词:非线性单调算子,变分不等式,Signorini问题,有限元逼近,收敛性,误差估计。     

含极大η-单调算子的广义非线性混合似变分包含组的扰动算法和稳定性

研究了一类含极大η-单调算子的广义非线性混合似变分包含组.依据不动点理论和极大η-单调算子的预解算子技巧,在Hilbert空间中提出了一种求这类变分不等式组的逼近解的扰动迭代算法,并证明了这类算法的收敛性和稳定性.所得结果是新的,并推广和统一了近期文献中的一些相关结论.     

变分不等式问题的解的存在性

对一般凸集约束下的变分不等式问题提出了一个新的例外簇概念.基于此概念,给出了变分不等式问题解存在的一个充分条件,此条件弱于许多已知的关于变分不等式问题的解的存在性条件.对于伪单调变分不等式问题,它是解存在的充要条件.对于P₀非线性互补问题,利用例外簇的概念,给出了其解存在的充分条件.     

集值混合变分不等式的一类自适应惯性投影次梯度算法

本文在实Hilbert空间上引入了一类求解集值混合变分不等式新的自适应惯性投影次梯度算法.在集值映射T为f-强伪单调或单调的条件下,我们证明了由该自适应惯性投影次梯度算法所产生的序列强收敛于集值混合变分不等式问题的的唯一解.     

Stability of Runge-Kutta-Pouzet methods for Volterra integro-differential equations with delays

This paper is concerned with the study of the stability of Runge-Kutta-Pouzet methods for Volterra integro-differential equations with delays. We are interested in the comparison between the analytical and numerical stability regions. First, we focus on scalar equations with real coefficients. It is proved that all Gauss-Pouzet methods can retain the asymptotic stability of the analytical solution. Then, we consider the multidimensional case. A new stability condition for the stability of the analytical solution is given. Under this condition, the asymptotic stability of Gauss-Pouzet methods is investigated.      

$n$-维中立型多时滞微分方程的稳定性分析

This paper is mainly concerned with stability analysis of neutral differential equations with multiple delays. Some criteria on instability, stability, asymptotic stability and exponential stability are obtained. The criterion on asymptotic stability is necessary and sufficient. Two examples are provided to illustrate the applications of our results. Some previous results are extended.     

Delay-Dependent Criteria for Robust Stabilization of Markovian Switching Networks with Time-Varying Delay

Abstract

A problem of feedback stabilization of hybrid systems with time-varying delay and Markovian switching is considered. Delay-dependent sufficient conditions for stability based on linear matrix inequalities (LMI's) for stochastic asymptotic stability is obtained. The stability result depended on the mode of the system and of delay-dependent. The robustness results of such stability concept against all admissible uncertainties are also investigated. This new delay-dependent stability criteria is less conservative than the existing delay-independent stability conditions. An example is given to demonstrate the obtained results.     

常微分方程数值方的法稳定性(英)

本文针对常微分方程数值方法稳定性问题，证明了一般方法的绝对稳定性定理，同时也指出了绝对稳定性条件的局限性．为了克服这种局限性，本文绘出了Jordan稳定性的概念，并建立了一个相应的判别定理．     

二元稳定网络的算法及模型

通过建立JW(Jackson-Wolinsky)规则之下二元稳定网络的等价条件, 给出其完整算法. 引入边支付后, 证明了增连接情形具有边支付的二元稳定网络集合是二元稳定网络集合与具有边支付的二元稳定网络集合的交集. 考察两个特定的网络模型, 系统分析了它们的二元稳定性.     

关于运用Liapunov函数的滞后型系统部分稳定性的注释

Sufficient conditions for the stability with respect to part of the functional differential equation variables are given. These conditions utilize Lyapunov functions to determine the uniform stability and uniform asymptotic stability of functional differential equations. These conditions for the partial stability develop the Razumikhin theorems on uniform stability and uniform asymptotic stability of functional differential equations. An example is presented which demonstrates these results and gives insight into the new stability conditions.     

The effect of density-dependent dispersal on the stability of populations

The nonlinear stability of two populations diffusing in a common bounded domain with nonlinear density-dependent dispersal of a general type is studied, under Robin boundary conditions. The stability and instability of the positive equilibrium are studied by the linear eigenvalues method. The nonlinear stability is studied with the Lyapunov direct method. In a particular case, global stability has been obtained.     

Stabilization of switched linear systems with time-delay in detection of switching signal

A feedback stabilization problem for switched linear systems with time-delay in detection of switching signal is formulated. First, online state feedback controller design method for asymptotic stability and exponential stability is given. Then, offline state feedback controller design method for asymptotic stability and exponential stability is given as well.     

Nonlinear Stability of General Linear Methods

This paper is devoted to a study of stability of general linear methods for the numerical solution of nonlinear stiff initial value problems in a Hilbert space. New stability concepts are introduced. A criterion of weak algebraic stability is established, which is an improvement and extension of the existing criteria of algebraic stability.