Lienard方程周期解、概周期解的存在性

本文考虑Ｌｉｅｎａｒｄ方程ｘ”十ｆ（ｘ）ｘ’＋ｇ（ｘ）＝ｅ（ｔ），我们得到：当且时，对于任意周期或概周期。数ｅ（ｔ），它有周期或概周期解．而对于Ｌｉｅｎａｒｄ方程ｘ”＋ｆ（ｘ）ｘ’＋ｃｘ＝ｅ（ｔ），我们得到：当ｃ＞０且时，对于任意周期、或概周期函数ｅ（ｔ），它有周期或概周期解．     

Bochner’s theorem and Stepanov almost periodic functions

Motivated by a renewed interest in generalizations of classical almost periodicity (originally due to Harald Bohr), we develop a theorem of Bochner within the framework of almost periodic functions in the sense of Stepanov. As a result we establish some conditions that guarantee the existence of Stepanov almost periodic solutions to differential equations with Stepanov almost periodic coefficients. Finally, we extend a now classic theorem of Favard originally stated for classical almost periodic functions to the Stepanov almost periodic case.      

一个A（f）≠M（f）的紧致系统（X，f）

本文证明，存在紧致系统，其几乎周期点集闭包不等于其测度中心．藉此，我们否定地回答了两个未解决的问题．     

ALMOST PERIODIC SOLUTIONS OF LASOTA-WAZEWSKA-TYPE DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT DELAYS AND ALMOST PERIODIC TIME DEPENDENCE

By using the concept of almost periodic "sequence", that is, a real valued function on Z satisfying the Bohr almost periodic condition, sufficient conditions are obtained for the existence of almost periodic solutions of Lasota-Wazewska-type differential equations with almost periodic time dependence.     

Almost periodicity,finite automata mappings,and related effectiveness issues

We introduce a class of eventually almost periodic sequences where some suffix is almost periodic (i.e., uniformly recurrent). The class of generalized almost periodic sequences includes the class of eventually almost periodic sequences, and we prove this inclusion to be strict. We also prove that the class of eventually almost periodic sequences is closed under finite automata mappings and finite transductions. Moreover, we obtain an effective form of this result. In conclusion we consider some algorithmic questions related to the almost periodicity.     

Almost periodic type solutions of differential equations with piecewise constant argument via almost periodic type sequences

The existence of almost periodic, asymptotically almost periodic, and pseudo almost periodic solutions of differential equations with piecewise constant argument is characterized in terms of almost periodic, asymptotically, and pseudo almost periodic sequences. Thus Meisters's and Opial's theorems are extended.     

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。     

Two unsolved problems on almost periodic type functions

We first show that like a scalar-valued case, a vector-valued weakly almost periodic function also satisfies the Parseval’s equality. Then we show that the space of vector-valued weakly almost periodic functions is a proper subspace of pseudo almost periodic functions. These solve two open questions on almost periodic type functions.     

含参数泛函微分方程概周期正解的存在性

研究了一类含参数泛函微分方程概周期正解的存在性问题.结合有界性及渐近概周期性获得了系统存在概周期正解的几组充分条件,并将结果应用于几类种群动力学模型,分别获得了系统在概周期环境下存在概周期解的一组充分条件.     

Almost periodic solutions for undamped nonhomogeneous delay-differential equations

We first establish a result giving conditions that certain undamped delay differential equations with almost periodic time dependence have unique almost periodic solutions. Using this result we obtain conditions that a second order scalar nonlinear delay differential equation with almost periodic forcing will have a unique almost periodic solution having saddle-type stability properties. These results use the method of averaging.

     

EXISTENCE OF ALMOST PERIODIC SOLUTIONS FOR DIFFERENCE SYSTEMS

1IntroductionAsisknown,therehavebeenquiteafewresu1tsontheexistenceofalrilostperiodicsolutionsforordinaryanddelaydifferentialstystems.However,tothebestofourknowledge,therehavenotappearedanycorrespondingresu1tsfOrevenordinarydifferencesystemssofar.Todealwithsuchproblems,wewilldefinethenotionoftheso-calleduni-formlyalmostperiodicsequencesbesidesthealmostsequencesandasymptoti-callyalmostsequences.Thenweprovidethecriteriaandthebasicpropertiesofuniformlyalmostperiodicsequenceswhichareneededinestabl…     

Almost periodic solutions of a discrete Lotka–Volterra competition system with delays

In this paper, we consider a discrete almost periodic Lotka–Volterra competition system with delays. Sufficient conditions are obtained for the permanence and global attractivity of the system. Further, by means of an almost periodic functional hull theory, we show that the almost periodic system has a unique strictly positive almost periodic solution, which is globally attractive. Some examples are presented to verify our main results.     

具有反馈控制的离散两种群竞争系统的概周期解

对于具有反馈控制的离散概周期两种群竞争系统的概周期解问题,进行了深入的讨论,得到了该系统存在唯一的一致渐近稳定概周期解的充分条件.     

Weighted pseudo almost periodic functions and applications

This Note introduces a new class of functions called weighted pseudo almost periodic functions, which generalize in a natural fashion the classical pseudo almost periodic functions due to C. Zhang. Properties of those weighted pseudo almost periodic functions are discussed including a composition result of weighted pseudo almost periodic functions, which plays a crucial role for the solvability of some weighted pseudo almost periodic semilinear differential and partial differential equations. To cite this article: T. Diagana, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

On a theorem of Favard

We obtain sufficient conditions for the existence of almost periodic solutions of almost periodic linear differential equations thereby extending Favard's classical theorem. These results are meant to complement previous results of the authors who have shown by means of a counterexample that the boundedness of all solutions is not, by itself, sufficient to guarantee the existence of an almost periodic solution to a linear almost periodic differential equation.

     

Hopfield神经网络概周期解的存在性和全局吸引性

该文研究Ｈｏｐｆｉｅｌｄ神经网络概周期解的存在性和全局吸性,获得了该网络存在唯一概周期解的充分条件和所有解收敛于此概周期解的充分条件。     

On the module containment of the almost periodic solution for a class of differential equations with piecewise constant delays

In the first part of this paper, we obtain a new property on the module containment for almost periodic functions. Based on it, we establish the module containment of an almost periodic solution for a class of differential equations with piecewise constant delays. In the second part, we investigate the existence, uniqueness and exponential stability of a positive almost periodic and quasi-periodic solution for a certain class of logistic differential equations with a piecewise constant delay. The module containment for the almost periodic solution is established.     

ON ALMOST PERIODIC SOLUTIONS OF AHIGHER ORDER ALMOST PERIODIC SYSTEM

1IntroductionConsiderthel'Ollowingdifferentialequationdx~~A(.t)x g(t,x),(l)dt.wherexeR",t6R,A(t)=(a,,(t)),,..istillnxncontinlloust'llllctiollmatrixinR,g(t,x)isanat-dimensionalcolltinuousfunctionvectorinRxR".Thepaper[l,21dealedwil;htheproblemontheexistence…     

Almost Periodic Solutions of Nonautonomous Linear Difference Equations

Explicit almost periodic solutions are obtained for a class of almost periodic linear difference equations. The stability characteristics of the almost periodic solution are investigated. The results are applied to a nonautonomous hyperbolic difference equation modelling the dynamics of a single species population in temporally varying environments.     

Lienard方程周期解、概周期解的存在性

本文考虑 Lienard方程 x″+f (x) x′+g(x) =e(t) ,我们得到 :当 -∞ 0且 0 相似文献