具连续变量脉冲中立型时滞差分方程的振动性

研究具连续变量脉冲中立型时滞差分方程△[y(t)-p(t)y(t-τ)]+q(t)y(t-σ)=0,t≠tk,y(tk+)-y(tk)=bky(tk),k=1,2,….通过构造辅助函数得到此函数与所研究方程解振动性的等价定理.从而获得方程所有解振动的两个充分性条件.     

一类具有脉冲的非线性时滞微分方程解的渐进性

研究了-类具有脉冲的二阶非线性时滞微分方程 (r(t))X'-p(t)x'(t) n∑i=1 qi(t)x(t-σi) f(t)=0, t≠tk, x(t k)-x(tk)=akx(tk),x1(t k)-x1(tk)=bkx1(tk), k∈z 的解的渐近性,并得到了一系列相关的充分条件.     

脉冲中立型时滞微分方程的正解的存在性

本文证明了线性脉冲中立型微分方程 [y(t)+p(t)y(t-τ)-r(t)y(t-ρ)]′+q(t)y(t-σ)=0,t≥0,t≠t_k, y(t_k~+)-y(t_k)=b_ky(t_k),k=1,2,…正解的存在性等价于一类非脉冲中立型方程正解的存在性,应用这一结果,建立了此类线性脉冲中立型微分方程正解存在性的若干充分条件。     

非振动解的渐近性（续）

讨论了非线性中立型微分差分方程[y(i) P(t)g(y(t-τ)]' Q（t)h(y(t-σ)=0的非振动解的渐近性，得到了方程非振动解在一定条件下趋于0， ∝，-∞的几个重要结论和一系列相关的结果。     

ON THE EXISTENCE OF NONTRIVIAL PERIODIC SOLUTIONS OF DIFFERENTIAL DIFFERENCE EQUATIONS

This paper cosiders the existence of nontrivial periodic solutions of the differentialdifference equationsx′(t)=-f(x(t-1)),x′(t)=-(f(x(t-1)+f(x(t-2))),and(x′(t)=f(x(t),y(t),x(t-1),y(t-1)),y′(t)=g(x(t),y(t),x(t-1),y(t-1)).)Some new existence criteria are obtained.     

含有n个滞量的三维微分差分方程组周期解的存在性

本文研究含有n 个滞量的三维微分差分方程组x(t)=sum from i=1 to ∞(1/i)f[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)]y(t)=sum from i=1 to ∞(1/i)g[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)](τ_i>0)z(t)=sum from i=1 to ∞(1/i)h[x(t),x(t-τ_i),y(t),y(t-τ_i),z(t),z(t-τ_i)]周期解的存在性,给出了方程组周期解周期的取值范围.推广并改进了文[1]的结果.     

一类二阶Emden-Fowler型中立型时滞微分方程的区间振动性

对一类二阶Emden-Fowler型中立型时滞积分方程(a(t)x′(t))′+q<,1>(t)|y(t-σ<,1>)|<'α>sgn x(t-σ<,1>)+g<,2>(t)|y(t-σ<,2>)|<'β>sgn y(t-σ<,2>)=0,利用Riccati技巧和积分平均法,给出了一些判定其解振动的充分判据.这些判据仅...     

变时滞混合随机微分方程的几乎必然指数稳定化（英文）

本文研究一类多维变时滞混合随机微分方程的几乎必然指数稳定性,方程具体形式:dy(t)=f(y(t-δ_1(t)),r(t),t)dt+g(y(t-δ_2(t)),r(t),t)dω(t),其中,δ_1(·),δ_2(·):R~+→[0,τ]表示变时滞,r(t)为一个Markov链.运用Lyapunov技巧,随机分析方法和BorelCantelli引理,该文证明了在一定的条件下,若此方程对应的混合随机微分方程:dx(t)=f(x(t),r(t),t)dt+g(x(t),r(t),t)dω(t)是几乎必然指数稳定的,则存在一个正常数τ,只要ττ,该方程也是几乎必然指数稳定的.这推广并改进了己有文献的一些结果.     

非线性中立型延迟微分方程稳定性分析

This paper is devoted to the stability analysis of both the true solution and the numerical approximations for nonlinear systems of neutral delay differential equations(NDDEs) of the general form y′(t)=F(t，y(t)，G(t，y(t-τ-(t))，y′(t-τ-(t)))). We first present a sufficient condition on the stability and asymptotic stability of theoretical solution for the nonlinear systems. This work extends the results recently obtained by A.Bellen et al. for the form y′(t)=F(t，y(t)，G(t，y(t-τ-(t))，y′(t-τ-(t)))). Then numerical stability of Runge-Kutta methods for the systems of neutral delay differential equations is also investigated. Several numerical tests listed at the end of this paper to confirm the above theoretical results.     

高维无穷时滞脉冲积分微分方程概周期解的存在唯一性

研究一类高维无穷时滞的非线性脉冲积分微分方程x′(t)=A(t)x(t)+∫-t∞C(t,s)g(s,x(s))ds+f(t,x(t-τ))+b(t),t≠tkΔx(t)=Bkx(t)+Ik(x(t))+γk,t=tk,k∈Z概周期解的存在性、唯一性问题.利用不动点原理和线性系统的指数二分性理论,建立了保证其概周期解存在性、唯一性的充分条件,得到了一些新的结果.     

一类非线性中立型脉冲时滞微分方程解的渐近性

该文研究具有正负系数的非线性中立型脉冲时滞微分方程获得了该方程的每一个解当t→∞时趋于一个常数的充分条件.     

二阶非线性中立型微分方程的振动性

利用Ho lder不等式研究一类非线性项具时滞的二阶中立型时滞微分方程{r(t)[y(t)+p(t)y(t-τ)]′2m+1}′+q(t)f[y(t-σ)]=0(t>t0)的振动性.给出了该方程的解振动的若干充分条件,所得结果推广了已有的相应结论.     

带分布时滞中立型微分方程正解的存在性

主要运用Banach压缩映像原理,研究了分布时滞中立型微分方程ddty(t)+∫abP(t,θ)y(t-θ)dθ+∫cdQ(t,θ)y(t-θ)dθ=0正解的存在性问题,获得了正解存在的充分条件,推广了相关文献的结果.     

Stability of sets for impulsive functional differential equations via Razumikhin method

In this paper, we consider the functional differential equation with impulsive perturbations

Anti-periodic solutions of nonlinear first order impulsive functional differential equations

The existence of anti-periodic solutions of the following nonlinear impulsive functional differential equations $$ x'(t) + a(t)x(t) = f(t,x(t),x(\alpha _1 (t)), \ldots ,x(\alpha _n (t))),t \in \mathbb{R},\Delta x(t_k ) = I_k (x(t_k )),k \in \mathbb{Z} $$ is studied. Sufficient conditions for the existence of at least one anti-periodic solution of the mentioned equation are established. Several new existence results are obtained.     

脉冲中立型时滞微分方程解的振动性

本文讨论一阶脉冲中立型时滞微分方程［ｙ（ｔ）＋Ｐｙ（ｔ－σ）］′＋Ｑ（ｔ）ｙ（ｔ－σ）＝０，ｔ０，ｔ≠ｔｋ，ｋ＝１，２，…，ｙ（ｔ＋ｋ）－ｙ（ｔ－ｋ）＝ｂｋｙ（ｔｋ），ｋ＝１，２，…，｛（Ｅ）这里τ，σ，Ｐ均为常数，τ＞０，σ＞０，Ｑ（ｔ）∈Ｃ（［０，∞），Ｒ＋），ｂｋ＞－１，ｋ＝１，２，…．分三种情况，Ｐ－１；－１＜Ｐ＜０；Ｐ＞０给出了方程（Ｅ）所有解振动的充分条件．     

Boundedness results for impulsive functional differential equations with infinite delays

In this paper, boundedness criteria are established for solutions of a class of impulsive functional differential equations with infinite delays of the form $$\begin{gathered} x'(t) = F(t,x( \cdot )), t > t^ * \hfill \\ \Delta x(t_k ) = I(t_k ,x(t_k^ - )), k = 1,2,... \hfill \\ \end{gathered} $$ By using Lyapunov functions and Razumikhin technique, some new Bazumikhin-type theorems on boundedness are obtained.