脉冲时滞差分方程物振动性

讨论脉冲时滞差分方程xn 1-xn pnxn-2=0,n≥0,n≠nk xnk 1-xnk=bkxnk,k=1,2,3…给出了方程所有解振动的充分条件。     

脉冲时滞差分方程的振动性

讨论脉冲时滞差分方程xn+1- xn +pnxn-2 =0 ,n≥ 0 ,n≠ nkxnk+1- xnk =bkxnk,k =1,2 ,3,…给出了方程所有解振动的充分条件     

含变时滞脉冲差分方程解的振动性

本文讨论含变时滞脉冲差分方程解的振动性,获得了方程所有解振动的充分条件.     

脉冲中立型时滞差分方程解的振动性

本文研究了一类脉冲中立型时滞差分方程的振动性,获得了该方程所有解振动的充分条件．     

脉冲时滞差分方程的振动性

讨论脉冲时滞差分方程｛ｘπ＋１－ｘπ＋ｐπｘπ－１＝０,ｎ≥０,ｎ≠ｎｋ;ｘπｋ＋１－ｘπｋ＝ｂｋｘπｋ,ｋ＝１,２,３…给出了方程所有解振动的充分条件。     

n阶时滞差分方程的边值问题

本研究n阶时滞差分方程的边值问题：     

一类具有正负系数的脉冲时滞差分方程的振动性

讨论了一类具有正负系数的咏冲时滞差分方程(?)解的振动性,给出了所有解振动的充分条件,推广和改进了已有的结果     

线性脉冲差分方程解的振动性与稳定性

本文主要建立了如下的线性脉冲差分方程｛xn 1-xn ∑mi=1pi(n)xn-ki=0,n≥0,n≠nj,xnj 1-xnj=bjxnj,j=1,2,…,解的振动和稳定性分别与一时滞差分方程振动性和稳定性等价,进而给出其振动性和稳定性显著充分条件。     

一类非线性差分方程的振动性

本文研究了二阶中立型时滞差分方程△「ａｎ△（ｘｎ＋ｐｎｘｇ（ｎ）」＋ｑｎｆ（ｘａ（ｎ））＝０的振动性,所得结果推广并改进了中立型时滞差分方程的一些已知结论     

时滞差分方程零解全局渐近稳定的充分必要条件及其应用

考虑一阶非线性时滞差分方程：　　　　　　其中　　　　　得到上述方程的零解是全局渐近稳定的充分必要条件，并将所得结果应用到一类非线性中立型差分方程。     

Stability of impulsive delay differential equations

In this paper, we introduce impulsive delayed matrix function and give its norm estimation. With the help of impulsive delayed Cauchy matrix and the variation of constants method, we obtain representation of solutions to linear impulsive delay differential equations. Moreover, we derive some sufficient conditions to guarantee the trivial solution is locally asymptotically stable. Finally, two examples are given to illustrate our theoretical results.     

求解非线性时滞脉冲双曲微分方程的隐式差分格式

构造了一类求解非线性时滞脉冲双曲型偏微分方程的隐式差分格式.在一定条件下,获得了该差分格式的唯一可解性、收敛性和无条件稳定性,且空间和时间均二阶精度.最后,数值实验表明了所得格式的精度和有效性.     

非线性脉冲差分方程解的稳定性

应用不等式估值法讨论了非线性脉冲时滞差分方程解的性质,并得到它的解的一致稳定性的一些充分条件.     

Periodic solutions of delay impulsive differential equations

We study the following semilinear impulsive differential equation with delay:

     

Stability of impulsive infinite delay differential equations

In this work, we consider the stability of impulsive infinite delay differential equations. By using Lyapunov functions and the Razumikhin technique, we get some results that are more general than ones given before. And in using the Razumikhin technique, we use a new technique that has been given by Shunian Zhang; we extend this technique to study impulsive systems. An example is also discussed in this work to illustrate the advantage of the results obtained.     

Ultimate boundedness of impulsive fractional delay differential equations

This paper concerns with the ultimate boundedness problem for impulsive fractional delay differential equations. Based on the impulsive fractional differential inequality, the boundedness of Mittag-Leffler functions, and the successful construction of suitable Lyapunov functionals, some algebraic criteria are derived for testing the global ultimate boundedness of the equations, and the estimations of the global attractive sets are provided as well. One example is also given to show the effectiveness of the obtained theoretical results.     

On generalized impulsive piecewise constant delay differential equations

A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications.     

Monotone iterative technique for impulsive delay differential equations

In this paper, by proving a new comparison result, we present a result on the existence of extremal solutions for nonlinear impulsive delay differential equations.     

Exponential stability of singularly perturbed impulsive delay differential equations

In this paper, the exponential stability of singularly perturbed impulsive delay differential equations (SPIDDEs) is concerned. We first establish a delay differential inequality, which is useful to deal with the stability of SPIDDEs, and then by the obtained inequality, a sufficient condition is provided to ensure that any solution of SPIDDEs is exponentially stable for sufficiently small ε>0. A numerical example and the simulation result show the effectiveness of our theoretical result.