EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS TO A HIGHER DIMENSIONAL PERIODIC SYSTEM WITH DELAY

In this paper, using fixed point theorem, we discuss a higher dimensional nonautonomous periodic system with delay and give some suffcient criteria for the existence and uniqueness of periodic solution. Our results extend and improve some results in previous researches.     

POSITIVE PERIODIC SOLUTION TO A CLASS OF NONLINEAR PERIODIC DIFFERENTIAL EQUATION WITH IMPULSES AND DELAY

In this paper, by using a fixed point theorem of Krasnoselskii, we study the positive periodic solution for a class of nonlinear periodic differential equation with impulses and delay. Firstly, definition of periodic solution and some lemmas are stated. Then some results of the existence of positive periodic solution about the equation are obtained.     

PERIODIC SOLUTION FOR DIFFUSIVE PREDATOR-PREY PATCH SYSTEMS WITH TIME DELAY AND PERIODIC STOCKING

In this paper, a three species difFusive predator-prey modei with functional response and periodic stocking is studied, where all parameters are time depen-dent. By using new theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.     

PERMANENCE,PERIODIC AND ALMOST PERIODIC SOLUTIONS OF NONAUTONOMOUS STAGE STRUCTURED POPULATION DYNAMICS WITH TIME DELAY AND DIFFUSION

A nonautonomous stage-structured two species model with time delay anddiffusion is considered. It is shown that the system is uniformly persistent undersome conditions. By discussing the independent subsystem, more brief sufficientconditions are drawn for a unique positive periodic solution which is globallyattractive and the existence of the positive almost periodic solution which isuniformly asymptotically stable by the Razumikhin function method.     

具脉冲效应的时滞周期捕食与被捕食系统正周期解的存在性

本文研究一类具脉冲效应的时滞周期捕食与被捕食系统，利用重合度理论中的方法，获得该系统至少存在一个正周期解的充分条件。     

PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS OF A NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH STAGE-STRUCTURE AND DELAY

In this paper, by using the comparing theorem, Razumikhin-type theorem and V-function method, we consider a nonautonomous predator-prey system with stage-structure and time-delay. We get the sufficient conditions for the uniform persistence and the solutions global attractivity of this system. For a periodic system, we obtain the existence and uniqueness of a positive periodic solution of this system. For an almost periodic system, we prove the existence and the uniform asymptotic stability of the almost periodic solutions of this system.     

周期生态系统的渐近性态

解关于初值的混合单调性是生态系统本身具有的特性，本文通过对一般周期生态系统所定义的混合单调算子的不动点性态的研究，得到正周期解的存在唯一性及其吸引性的一般性结论。该结论包含了许多已知的结果。     

MONOTONICITY AND EXISTENCE OF ALMOST PERIODIC SOLUTION

1IntroductionOpial[11discoveredsuchafact:ifthealmostperiodicequationX'=f(x,t)x?tERandallsystemsinitshullsatisfytheexistenceanduniquenesstheoremandfismonotonicinxtthenthesystemhasanalmostperiodicsolutionwhenithasaboundedsolution.ltisnaturallyexpectthatitco…     

指数型二分性和周期系统的周期解

先讨论指数型二分性成立的条件，在某种意义下推广了Ｌａｚｅｒ关于二分性的结果，之后，我们用该结论探讨Ｌａｓｏｔａ－Ｏｐｉｕｌ方程及方程ｘ＝ｆ（ｔ，ｘ），ｆ（ｔ＋ｗ，ｘ）＝ｆ（ｔ，ｘ），ｆ（ｔ，ｘ）∈Ｃ’（Ｒ＊Ｒ＾ｎ，Ｒ＾ｎ）的周期解的存在性，推广了文「２」的主要结果，并得到一些新的结果。     

PERIODIC AND ALMOST PERIODIC SOLUTIONS OF A CERTAIN INFINITE DELAY INTEGRAL EQUATION

In this paper,by using successive approximation method and fixed-point theorem,we discuss a class of infinite delay integral equation and obtain some sufficient conditions which guarantee the existence and uniqueness of the peri- odic and almost periodic solutions of the system.     

非线性退化时滞系统的周期解

本文利用不动点方法研究两类非线性退化时滞系统的周期解问题,获得了这两类 系统存在周期解的若干充分条件。     

FORCED ALMOST PERIODIC OSCILLATION OF SECOND ORDER NONLINEAR EQUATION

1 IntroductionConsider equation of the Duffing fOrmX" cx' g(x) = p(t) (1)where c is a constant, p and g are continuous functions defined on (--oo, oc).In the early years of the l990's, some authors investigated the existence andstability of periodic solution of system (1), when p(t) is a periodic function(see [1],[2]).In this paper, we consider the situation in where p(t) is an almost periodicfunction. Under some conditions, we prove the existence and uniqueness ofalmost periodic soluti…     

GLOBAL EXISTENCE OF POSITIVE PERIODIC SOLUTION FOR A NEUTRAL DELAY COMPETITIVE SYSTEM

In this paper, by means of Mawhin's coincidence degree theory and somenew techniques, sufficient conditions for the global existence of positive periodicsolution to a class of neutral type competitive system with delays are obtained.     

ALMOST PERIODIC SOLUTIONS OF SINGLE POPULATION MODELS WITH ALMOST PERIODIC ENVIRONMENT

ＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＯＦＳＩＮＧＬＥＰＯＰＵＬＡＴＩＯＮＭＯＤＥＬＳＷＩＴＨＡＬＭＯＳＴＰＥＲＩＯＤＩＣＥＮＶＩＲＯＮＭＥＮＴＨｅＣｈｏｎｇｙｏｕ（ＮａｎｊｉｎｇＵｎｉｖｅｒｓｔｙ）（何崇佑）南京大学，邮编：２１０００８Ａｂ...     

EXISTENCE OF POSITIVE PERIODIC SOLUTION OF MUTUALISM SYSTEM WITH INFINITE DELAYS

In this paper, by using Mawhin coincidence degree, some sufficient conditions are obtained for the global existence of positive periodic solution of a mutualism system with infinite delays. Our results generalize those of Yang etc. [8] and Gopalsamy and He [7].     

ANALYSIS OF THE PERIODIC BAUTIN CHEMICAL OSCILLATION SYSTEM

1IntroductionIfl1939,N.N.Bautill[1,2]studiedasystemofcouplednolllilleardifferelltialequations'whichhasseverall'eaturcsofinterestforthestudyofchemicaloscillations.M*-L.Sinoes[3]showedthatfurthertheBautinsystemisaveryadequatemodelforchemicaloscillations,the…     

EXISTENCE AND ATTRACTIVITY OF ALMOST PERIODIC SOLUTION FOR HOPFIELD NEURAL NETWORKS WITH VARIABLE COEFFICIENTS

This paper is to study the existence and attractivity of almost periodic solution for Hopfield-Type delay cellular neural networks(HDCNNs) with variable coefficientsby combining the theory of the exponential dichotomy and Lyapunov functionals method and combine with some analysis techniques. We obtain some sufficient conditions to ensure the networks to have a unique almost periodic solution, and all other solutions converge to this solution.     

一种广义周期Besov类的多元周期多项式样条逼近

本文证明多元多项式周期样条空间是某些多元周期光滑函数类的关于Kolmogorov n-宽度的弱渐近极子空间．给出了广义周期Besov类的一种推广，得到了空间元素的一种表示定理，不仅给出了一种多元周期多项式样条算子．而且证明了所得的结果．     

人口动力学中一类含时滞周期反应—扩散方程的正周期解分歧

本文研究人口动力学中一类含时滞周期反应-扩散方程的正周期解问题;利用紧算子的全局分歧结果给出了这个方程正周期解存在的充分必要条件。     

EXISTENCE OF POSITIVE PERIODIC SOLUTION FOR A DELAYED PERIODIC PREDATOR-PREY MODEL OF IVLEV TYPE

A periodic coefficients predator-prey system of Ivlev type with both discrete and continuous time delay is investigated. A sufficient condition of the existence of positive periodic solution is established for the system by using the continuation theorem of coincidence degree theory.