PERIODIC SOLUTIONS FOR A CLASS OF DEGENERATE NEUTRAL PERIODIC SYSTEM WITH DELAY

In this paper, using fixed point method, discusses the problem of periodic solution for a class of degenerate neutral periodic system with delay, and obtains some sufficient conditions for the existence and uniqueness of periodic solution of the system, the result extends and improves some results of paper [1-2].     

一类高维滞后型泛函微分方程的周期解

本文研究一类滞后型函数分方程的周期解问题，利用指数型二分性和不动点定理，在较广泛的条件下证明了该方程的周期解的存在性及唯一性，推广并改进了文[1-3]的主要结果     

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.     

具有无限时滞的退化微分系统的周期解

考虑具有无限时滞的中立型退化微分系统E(t)d/dt[x(t) -∫t-∞C(t,s)x(s)ds]=A(t)x(t)+f(t,x(t-τ(t))+b(t)的周期解的存在性和唯一性问题,利用线性系统指数型二分性理论和Krasnoselsku不动点定理研究此系统,并通过技巧性代换获得了保证其周期解存在性和唯一性的充分性条件,得到了一些新的结果,推广了相关文献的主要结果.     

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.     

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.     

退化时滞微分方程的周期解问题

本文讨论退化时滞微分方程的周期解问题．特别地，我们给出二维退化滞后微分方程的周期解的存在性问题，并在最后举例说明其应用。     

EXISTENCE OF POSITIVE PERIODIC SOLUTION TO A CLASS OF NEUTRAL DELAY COMPETITION MODEL

By means of the theory of coincidence degree, sufficient condition for the existence of positive periodic solution to certain neutral delay competition model is obtained.     

一类具时滞的中立型Lotka-Volterra模型的周期解

讨论了n种群时滞的中立型Lotka Volterra生态模型。利用新的重合度理论中连续性定理 ,得到了该模型正周期解存在性的充分条件     

THE EXISTENCE OF ALMOST PERIODIC SOLUTION TO A CLASS OF ALMOST PERIODIC DIFFERENTIAL SYSTEM

By means of the fixed point theorem and exponential dichotomy, in this paper we investigate the existence of almost periodic solutions to a class of n-dimensional almost periodic systems, which is more general than the systems in [1-2]. We generalize and improve some results in [3].     

POSITIVE PERIODIC SOLUTION TO SECOND-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION WITH MIXED DELAY

We discuss two types of second-order neutral functional differential equations with mixed delay in this paper. By applying Krasnoselskii's fixed-point theorem, some results about the existence of positive periodic solution to the systems are obtained, which complement the previous known results.     

PERIODIC SOLUTIONS TO A KIND OF NEUTRAL DIFFERENTIAL SYSTEM:VIA (h,k)-DICHOTOMY

In this paper, based on the theory of (h, k)-Dichotomy of linear system and Kras-noselskii’s fixed point theorem, we study the existence of periodic solutions to a neutral differential equation. Some new sufficient conditions are obtained to guarantee the existence and uniqueness of T-periodic solution to the equation.     

ON THE EXISTENCE OF ALMOST PERIODIC SOLUTIONS OF SOME DELAY DIFFERENTIAL EQUATIONS

By means of exponential dichotomy, this paper investigates the existence of almost periodic solutions of some delay differential equations.     

PERIODIC SOLUTIONS TO NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

A new and convenient method is used to study the existence of periodic solutions to neutral functional differential equations with infinite delay. A new criterion for the existence of periodic solutions is obtained in this paper.     

PERIODIC SOLUTIONS FOR HIGHER ORDER DELAY FUNCTIONAL DIFFERENTIAL EQUATION OF NEUTRAL TYPE WITH LINEAR RESTORING TERMS

Using the theory of coincidence degree, the authors studied the existence of periodic solutions for higher order delay functional differential equations of neutral type with restoring terms and some new results for the existence of periodic solutions have been obtained.     

OSCILLATION CRITERIA FOR A CLASS OF HIGHER ORDER NEUTRAL DIFFERENTIAL EQUATIONS

We establish a new oscillation condition for even order neutral type differential equation of the following formwhere f is continuous and exists 1 ≤ k ≤ m(?)(t) ≡ Tk(t), a, (?)i ∈ C([0, ∞], R), i = 1, …,m. such that 0 ≤ a(t) ≤ L and     

PERIODIC SOLUTION TO A CLASS OF SECOND ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION WITH A STATEMENT-DEPENDENT DEVIATION VARIABLE

We obtain sufficient conditions for the existence of periodic solution to a class of second order neutral functional differential equation,using continuation theorem of the coincidence degree.     

具有变量时滞的周期微分系统的周期解

本文考虑周期微分系统x(t) =A(t,x(t- r1(t) ) ) x(t) + f (t,x (t- r2 (t) ) )的 T-周期解的存在性问题 ,其中 (t,x)∈R× Rn,A(t,x)是 n× n连续矩阵函数 ,f(t,x)是 n维连续向量函数 ,时滞 ri(t) (i=1,2 )是连续函数 ,且 A(t+ T,x) =A(t,x) ,f(t+ T,x) =f(t,x) ,ri(t+ T) =ri(t) (i=1,2 ) ,常数T>0 .本文利用不动点方法 ,建立了保证系统存在 T-周期解的充分条件 ,推广了文 [1- 3]的相关结果 .     

EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTION TO A CLASS OF HIGHER DIMENSIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper,using fixed point method,we discuss the problem of periodic solution to a class of higher dimensional functional differential equation.Our results extend and improve some results of the previous researches.     

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。