CONVERGENCE OF SOLUTIONS FOR A CLASS OF DIFFERENCE EQUATIONS WITH VARIABLE DELAY

Ｃｏｎｓｉｄｅｒｔｈｅｄｉｆｅｒｅｎｃｅｅｑｕａｔｉｏｎｗｉｔｈａｖａｒｉａｂｌｅｄｅｌａｙｘｎ－ｘｎ－１＝Ｆ（ｘｎ，ｘｒ（ｎ），ｎ＝ｎ０，ｎ０＋１，…（１）ｗｈｅｒｅ（Ｈ１）：Ｆ∈Ｃ（Ｒ×Ｒ，Ｒ），Ｆ（ｕ，ｖ）ｉｓｄｅｃｒｅａｓｉｎｇｗｉｔｈｒｅｓ...     

关于一类离散时间神经网络模型的稳定性

考虑一类离散时间神经网络模型的稳定性，得到了模型的平衡解是渐近稳定的充分必要条件。     

高阶非线性混合中立型方程的振动性

考虑ｎ阶混合中立型方程，建立了几个比较定理。在一定的条件下，可将中立型方程的振动性问题转化为相关的非中立型方程的振动性问题来处理。     

具有连续变量的差分方程的振动性

本文建立了具有连续交量差分方程的振动性判据，其结果改进了文献中的某些已知结果．     

EXISTENCE OF SOLUTIONS IN THE FUTURE FOR A CLASS OF NONLINEAR DIFFERENTIAL SYSTEMS

1 IntroductionThe problem cited in the title above is an old problem, and has been studiedby many authors. Some good results can be found in [1-5] and referencesquoted therein.In this paper we are concerned with this problem for the nonlinear differential systemJ 1 -- ':)>.--,,<,> ~ F(x), (1 l)where E,P, F, q and g are continuous real functions defined on R. Clearly, ifputting E(z) = z, p(y) = y and q(y) H 1, then (1.1) gives the well-knownLi6nard system{ 1:,.:<">, (l 2)Therefore, (1.1) is…     

一类具有媒体报道的传染病模型

将媒体报道量M视为时间t的函数,利用非连续函数β/(1+εMI)来刻画媒体报道对传染率的影响,建立了一个分段光滑的SIM传染病模型,给出了模型的非负平衡点的存在性。利用微分方程线性化稳定性理论分析,得到了系统的各平衡点局部稳定的阈值条件,并进一步利用Poincare-Bendixon定理给出了正平衡点全局渐近稳定的充分条件。     

CONVERGENCE OF A DISCRETE SYSTEM

Consider a nonlinear discrete-time system, we obtain a sufficient condition such that all solutions of this system converge to the equilibrium.     

一类中立型时滞微分方程解的渐近性

本文考虑一类非线性中立型时滞微分方程解的渐近性，给出了方程的解收敛于常数的结果．所得结论改进和推广了文献中的某些已知结果．     

一类中立型脉冲时滞生物模型的正周期解(英文)

运用严格集压缩映射不动点定理,讨论得到了一类中立型脉冲时滞生物模型正周期解存在的充分条件.我们去掉了文[6,7,12-14]周期解存在的一些条件,推广了对应的结果.     

Nontrivial Homoclinic Solutions for Second-Order p-Laplacian Differential System with Impulsive Effects

The existence of homoclinic solutions for the second-order p-Laplacian differential system( ρ( t) Φp( u'( t))) '-s( t) Φp( u( t))+ λf( t,u( t)) = 0 with impulsive effects Δ( ρ( tj) Φp( u'( tj))) = Ij( u( tj)) is studied. By using three critical points theorem and variational methods, the sufficient condition is established to guarantee that this p-Laplacian differential system with impulsive effects has at least one nontrivial homoclinic solution. Besides,an example is presented to illustrate the main result in the end of this paper.