Uniformly Asymptotic Stability and Existence of Almost Periodic Solutions for Functional Differential Equations

Ｉｔｉｓｗｅｌｋｎｏｗｎｔｈａｔｆｏｒａｎａｌｍｏｓｔｐｅｒｉｏｄｉｃｏｒｄｉｎａｒｙｄｉｆｅｒｅｎｔｉａｌｓｙｓｔｅｍｔｈｅｅｘｉｓｔｅｎｃｅｏｆａｕｎｉｆｏｒｍｌｙａｓｙｍｐｔｏｔｉｃａｌｙｓｔａｂｌｅｂｏｕｎｄｅｄｓｏｌｕｔｉｏｎｉｍｐｌｉｅｓ...     

The Existence of Almost Periodic Solutions of Second Order Neutral Differential Equations with Piecewise Constant Argument

51.Intr0ducti0nInthispaper,weconsidertheexistenceofalmostperiodicsoluti0nsforthefoll0wingneutralfunctionaldifferentialebuationwithpiecewiseconstantargument:wherep,qarenonzeroconstants,p(t)lsanalmostper1odicfunctlon,g:RXRXR-Risanalm0stperiodicfunctionintanduniformlyonRXR,andL.jstandsforthegreatest-integerfunction.Notethatforanyintegern,if2n-10)andtheequations(1),(2)areadvanced(orretardedrespectively).Differentialequationswithpiecewiseconstantar…     

一类微分差分方程的周期解

本文研究微分差分方程ｘ＇（ｔ）＝－ｆ（ｘ（ｔ），ｘ（ｔ－τ１））－ｆ（ｘ（ｔ），ｘ（ｔ－τ２））－．．．－ｆ（ｘ（ｔ），ｘ（ｔ－τｎ））非平凡周期解的存在性问题，得到了一些判别准则，推广和改进了文［１－４］的工作。     

带逐段常变量的微分方程的概周期解

本文研究相关差分方程的概周期序列解,并以此为工具得出带逐段常变量的微分方程的概周期解的若干存在性定理．     

Stability of Periodic Solutions of Ordinary Differential Equations in Banach Spaces

§１．ＤｅｆｉｎｉｔｉｏｎｓａｎｄＮｏｔａｔｉｏｎｓＬｅｔＥｂｅａｒｅａｌＢａｎａｃｈｓｐａｃｅ,ａｎｄｌｅｔｘ,ｙ∈Ｅ．Ｔｈｅｄｉｒｅｃｔｉｏｎａｌｄｅｒｉｖａｔｉｖｅ［ｘ,ｙ］－ｏｆｘａｎｄｙｉｓｄｅｆｉｎｅｄｂｙ（ｆｏｒｍｏｒｅｄｅｔａｉｌｓｓ...     

Almost Periodic Solutions of Neutral Differential Difference Equations with Piecewise Constant Arguments

In this paper, we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods. Received February 18, 2000, Accepted September 30, 2000.     

脉冲Hematopoiesis模型的概周期解

获得了脉冲Hematopoiesis模型{Q（t）=-c（t）Q（t）-α（t）Q（t）/1＋Q（t）＋β（t）∫^τ0F（u）Q（t-u）/1＋Q（t-u）ds △Q（tk）=αk（t）Q（t）k＋bk（t） 概周期解的存在性与指数稳定性．     

Monotone Method for Second Order Periodic Boundary Value Problems and Periodic Solutions of Delay Difference Equations

In this article, we employ monotone iterative technique to study the existence of solutions for second order periodic boundary value problem and periodic solutions of delay difference equations.     

On the Periodic Character of Some Difference Equations

We consider positive solutions of the following difference equation x n =max A x n m k , B x n m m , n =0,1,…, where A , B are any positive real numbers and k , m are any positive integers. We prove that every positive solution is eventually periodic and determine the period in terms of the parameters A , B , k , and m .     

On Periodic Solutions of Second Order Linear Difference Equations

In this paper, we apply a new procedure initially developed in Refs. [H. El-Owaidy and H.Y. Mohamed. "On the periodic solutions for nth order difference equations". Journal of Applied Mathematics and Computation , (to appear); "The necessary and sufficient conditions of existence of periodic solutions of nonautonomous difference equations". Journal of Applied Mathematics and Computation , (to appear)] to simplify the use of Carvalho's method to the case of discrete difference equations, in order to find the periodic solutions of second order linear difference equations. We can also find the complex periodic solutions.     

差分方程解的稳定性、有界性及概周期解的存在性

作者通过Liapunov泛函建立了一类高维差分方程解一致稳定、一致渐近稳定及指数渐近稳定的充要条件. 此外, 作者还证明了解的一致渐近稳定性蕴含解的有界性, 同时也给出了概周期差分方程存在概周期解的一个充分条件.     

一类时滞反应扩散方程的周期解和概周期解

通过构造上、下控制函数，结合上、下解方法及相应的单调迭代方法研究了一类时滞反应扩散方程，证明了在反应项非单调时，如果一雏边值问题存在一对周期（或概周期）上、下解，则方程一定存在唯一的周期（或概周期）解．并给出了二维边值问题周期（或概周期）解存在唯一性的充分条件．推广了已有的一些结果。     

Periodic Solutions for Nonlinear Diferential Equations

ＰｅｒｉｏｄｉｃＳｏｌｕｔｉｏｎｓｆｏｒＮｏｎｌｉｎｅａｒＤｉｆｅｒｅｎｔｉａｌＥｑｕａｔｉｏｎｓＣｏｎｇＦｕｚｈｏｎｇ（从福仲）（ＯｆｆｉｃｅｏｆＭａｔｈｅｍａｔｉｃｓ，８６００３Ｕｎｉｔ，Ｃｈａｎｇｃｈｕｎ，１３００２２）ＭａｏＤｏｎｇｍｉｎｇ（...     

Periodic Solutions of Nonautonomous Discrete Predator-Prey System of Lotka-Volterra Type

A sufficiency criterion is established for the existence of positive periodic solutions of a nonautonomous discrete time predator-prey system of Lotka-Volterra type. Our approach is based on the coincidence degree and the related continuation theorem as well as some priori estimates.     

概周期解的存在性、唯一性与稳定性

本文给出了一些保证微分方程的周期解和概周期解的存在性、唯一性、稳定性与不稳定性的充分性条件及周期解的存在范围估计式.所得结果推广[1]的主要结果及[2-6]的有关结果.     

Global Behaviour of Solutions of Nonlinear Delay Difference Equations*

In this paper global asymptotic stability and asymptotic behaviour of solutions of nonlinear delay difference equations has been studied and a few sets of sufficient conditions for global asymptotic stability are derived.     

Bouligand Dimension of Fractal Curve of Almost Periodic Series

in this paper, we obtain the calculating formulas for Bouligand dimension offractal curves represented by some almost periodic function series.     

Existence of an Almost Periodic Solution in a Difference Equation with Infinite Delay

In order to obtain the existence of an almost periodic functional difference equation x(n + 1) = ?(n,x_n ),n ∈ Z ⁺ and where x_n is defined by x_n (s) = x(n + s) for s ∈ Z ^?, on an axiomatic phase space B, we consider a certain stability property, which is referred to as BS-stable under disturbances from Ω(?) with respect to K, this stability implies ρ-stable under disturbances from Ω(?) with respect to compact set K.     

Bounded and Almost Periodic Solutions of Linear High-Order Hyperbolic Equations

The present paper is devoted to investigating high-order strictly hyperbolic operators with nearly constant coefficients. The invertibility of these operators in spaces of functions uniformly bounded or almost periodic in time is established, provided the symbol of the operator in question has no roots in an open strip containing the real line. Under the additional condition that the strip coincides with a half-plane, exponentially decaying solutions of the nonhomogeneous equation with right-hand side of exponential decay are constructed. In the case of equations with constant coefficients the necessity of the derived conditions is proved. The results of this paper were announced without proofs in [SV].