Schwarzschild时空中带记忆项的波动方程耦合方程组解的奇性

本文通过建立滞后型脉冲泛函微分方程饱和解的存在唯一性定理,在广义常微分方程与滞后型脉冲泛函微分方程等价的基础上,研究了滞后型脉冲泛函微分方程关于一致有界性的Lyapunov逆定理.     

滞后型脉冲泛函微分方程周期解的存在性

本文借助Mawhin重合度理论中的延拓定理和广义常微分方程周期解的存在性,在滞后型脉冲泛函微分方程与广义常微分方程存在等价关系的条件下,建立了滞后型脉冲泛函微分方程周期解的存在性定理.     

脉冲滞后泛函微分方程的平均化［英文］

本文利用广义常微分方程的平均化定理,建立脉冲滞后泛函微分方程周期及非周期的平均化定理。     

脉冲滞后泛函微分方程的平均化(英文)

本文利用广义常微分方程的平均化定理,建立脉冲滞后泛函微分方程周期及非周期的平均化定理。     

脉冲积分——微分方程的几个渐近稳定性结果

本文运用 Liapunov泛函法对于在可变时间具有脉冲扰动的 Volterra型泛函微分方程建立几个渐近稳定性结果 .它们与关于脉冲常微分方程、积分微分方程的已有结果的区别在于更着重反映脉冲对稳定性的影响     

一类具有无穷时滞中立型非稠定脉冲随机泛函微分方程积分解的存在性

本文讨论了一类具有无穷时滞中立型非稠定脉冲随机泛函微分方程,利用Sadovskii不动点原理等工具得到了其积分解的存在性,给出其在一类二阶无穷时滞中立型非稠定脉冲随机偏微分方程积分解的存在性中的应用.     

无限滞后测度泛函微分方程的平均化

本文研究了无限滞后测度泛函微分方程的平均化.利用广义常微分方程的平均化方法,在无限滞后测度泛函微分方程可以转化为广义常微分方程的基础上,获得了这类方程的周期和非周期平均化定理,推广了一些相关的结果.     

非局部条件下的脉冲中立型泛函微分方程

利用Sadovskii不动点定理研究了一类脉冲中立型泛函微分方程，证明了适度解的存在性．最后，给出了上述问题在偏微分方程方面的一个应用．     

一类脉冲随机泛函微分方程的分布稳定性分析

本文研究了一类脉冲随机泛函微分方程的分布稳定性问题.利用弱收敛方法、伊藤公式和一些常用的随机分析技巧,得到了一类脉冲随机泛函微分方程依分布稳定的一个充分条件,并且举例说明了结论的有效性,推广了随机泛函微分方程稳定性的相关结果.     

无限滞后测度泛函微分方程的平均化（英文）

本文研究了无限滞后测度泛函微分方程的平均化.利用广义常微分方程的平均化方法,在无限滞后测度泛函微分方程可以转化为广义常微分方程的基础上,获得了这类方程的周期和非周期平均化定理,推广了一些相关的结果.     

脉冲泛函微分方程的整体解

本文给出了非线性脉冲泛函数微分方程整体解的存在性的一些结果。     

Global exponential stability of impulsive differential equations with any time delays

The main objective of this letter is to further investigate the global exponential stability of a class of general impulsive retarded functional differential equations. Several new criteria on global exponential stability are analytically established based on Lyapunov function methods combined with Razumikhin techniques. The obtained results extend and generalize some results existing in the literature. An example, along with computer simulations, is included to illustrate the results.     

A new continuous dependence result for impulsive retarded functional differential equations

We consider a large class of impulsive retarded functional differential equations (IRFDEs) and prove a result concerning uniqueness of solutions of impulsive FDEs. Also, we present a new result on continuous dependence of solutions on parameters for this class of equations. More precisely, we consider a sequence of initial value problems for impulsive RFDEs in the above setting, with convergent right-hand sides, convergent impulse operators and uniformly convergent initial data. We assume that the limiting equation is an impulsive RFDE whose initial condition is the uniform limit of the sequence of the initial data and whose solution exists and is unique. Then, for sufficient large indexes, the elements of the sequence of impulsive retarded initial value problem admit a unique solution and such a sequence of solutions converges to the solution of the limiting Cauchy problem.     

Non-periodic averaging principles for measure functional differential equations and functional dynamic equations on time scales involving impulses

We present a non-periodic averaging principle for measure functional differential equations and, using the correspondence between solutions of measure functional differential equations and solutions of functional dynamic equations on time scales (see Federson et al., 2012 [8]), we obtain a non-periodic averaging result for functional dynamic equations on time scales. Moreover, using the relation between measure functional differential equations and impulsive measure functional differential equations, we get a non-periodic averaging theorem for these equations. Also, it is a known fact that we can relate impulsive measure functional differential equations and impulsive functional dynamic equations on time scales (see Federson et al., 2013 [9]). Therefore, applying this correspondence to our averaging principle, we obtain a non-periodic averaging theorem for impulsive functional dynamic equations on time scales.     

Cone-valued Lyapunov functions and stability for impulsive functional differential equations

The stability criteria in terms of two measures for impulsive functional differential equations are established via cone-valued Lyapunov functions and Razumikhin technique. The stability can be deduced from the (Q₀,Q)-stability of comparison impulsive differential equations. An example is given to illustrate the advantages of the results obtained.     

Existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects

This paper deals with a new existence theory for single and multiple positive periodic solutions to a kind of nonautonomous functional differential equations with impulse actions at fixed moments by employing a fixed point theorem in cones. Easily verifiable sufficient criteria are established. The paper extends some previous results and reports some new results about impulsive functional differential equations.     

脉冲泛函微分方程实用稳定性的一个比较定理

考虑一类脉冲泛函微分方程的实用稳定性，利用锥值李亚普诺夫函数方法，建立了脉冲泛函数微分方程与脉冲常微分方程的实用稳定性之间的比较定理。     

Exponential stability of impulsive stochastic functional differential equations

In this paper, we investigate the pth moment and almost sure exponential stability of impulsive stochastic functional differential equations with finite delay by using Lyapunov method. Several stability theorems of impulsive stochastic functional differential equations with finite delay are derived. These new results are employed to impulsive stochastic equations with bounded time-varying delays and stochastically perturbed equations. Meanwhile, an example and simulations are given to show that impulses play an important role in pth moment and almost sure exponential stability of stochastic functional differential equations with finite delay.     

STABILITY OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

In this paper,the stability of a class of impulsive functional differential equations with infinite delays is investigated. A uniform stability theorem and a uniform asymptotic stability theorem are established.