On Periodic Solutions of the Periodic

By treating the periodic Riccati equation ${\rm\dot{z}=a(t)z^2+b(t)z+c(t)}$ as a dynamical system on the sphere S, the number and stability of its periodic solutions are determined. Using properties of Moebius transformations, an exact algebraic relation is obtained between any periodic solution and any complex-valued periodic solution. This leads to a new method for constructing the periodic solutions.     

On Periodic Solutions of Linear Control Systems

We prove a theorem of the alternative concerning periodic solutions of linear control systems. We show that, if the attainable sets have nonempty interior, then the main condition assumed in Theorem 4.2 of Ref. 1 (a tangential condition) can be weakened and simplified, and a stronger conclusion can be obtained.     

一类积分微分包含的周期解

研究了一类积分微分包含的周期解,利用Kakutani不动点定理和Tichonoff不动点定理给出了凸和非凸两种情形下周期解存在的充分条件.     

关于非自治Lagrange系统的周期解

用变分方法研究非自治Lagrange系统周期解的问题转化为研究Lagrange作用泛函的临界点问题。对Lagrange系统，人们用变分方法已经获得了一系列可解性条件，但是除在超二次条件下，Lagrange作用泛函都是下方有界的。这里的目的是给出Lagrange作用泛函无界的Lagrange系统周期解的其它可解性条件，这时的主要困难是对应的Lagrange作用泛函不再是下方有界的。这里用临界点理论中的鞍点定理得到了Lagrange系统周期解的存在性。     

On Periodic Viable Solutions of Differential Inclusions

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On Periodic Solutions of a Class of Differential Equation with Periodic Coefficients

51.IntroductionandtheLemmas.Thefollowingequationy'=f(t,y)=A(t)y" B(t)y C(t)(m22,meN)(l.1)(WhereA(t),B(t)andC(t)areallcontinuousT-periodicfunctions,TXO)isencounteredinseveralappliedareas,sincethisequationplaysanimportantroleinthestudiesofnonlinearos-cillation,fluidmechanicsandthequalitativetheoryofordinarydifferentialequation.Whenm=2,(1.1)isthefamousRiccatiEqation.In1979,ProfessorQinYuanxunansweredthequestionthatunderwhatconditionsRiccatiEquationwithperiodiccoefficientshasthecontinu-ous…     

On Periodic Solutions of a Beam Vibration Equation

We prove a theorem on the existence of countably many periodic solutions of a quasilinear vibration equation for a freely supported I-beam.     

On Periodic Solutions of Nonlinear Functional Differential Equations

Sufficient conditions are established for the existence and uniqueness of an -periodic solution of the functional differential equation where f is a continuous operator acting from the space of n-dimensional -periodic continuous vector functions into the space of n-dimensional -periodic and summable on [0,] vector functions.     

具有时滞的高维周期系统的周期解

本文研究具有时滞的高维周期系统x'(t)=A(t,x(t))x(t)+f(t,x(t-τ))与x'(t)=gradG(x(t))+f(t,x(t-τ))的周期解,利用重合度理论,得到保证其存在周期解的充分条件.作为应用,建立了一类对数种群模型周期正解的存在性.     

一阶非线性泛函微分方程的周期解

本文研究了一阶非线性泛函微分方程的周期解,得到了周期解存在唯一的一些充分条件,推广和改进了这方面的已有结果。     

关于微分包含的周期解及其应用

研究了一类发展包含的周期问题,其结果应用于建立一类半线性微分包含周期解的存在性定理．给出了半线性微分包含端点解的存在性定理和强松驰定理,并且应用于周期反馈控制系统．     

一类非齐次时滞微分方程概周期解的存在性

该文研究一类非齐次时滞微分方程的概周期解, 结合运用指数二分法, 给出了系统存在概周期解的一组充分条件.     

关于退化中立型微分方程的周期解

讨论了退化中立型微分方程的周期解问题,给出了周期解存在性的条件和二维退化中立型微分方程周期解存在的代数判据,并且举例说明了其应用.     

一个描述血吸虫病的数学模型的周期解

研究一个描述血吸虫病的周期微分方程模型dx/dt=-rx+A/S(t)y,dy/dt=-δ(t)y+B(S(t)-y) x2/1+ x.数值计算发现该系统同时具有渐近稳定的零解和一个正周期解.通过证明该系统解的有界性,并在一个函数空间上构造单调有界序列,进而证明了在一定条件下正周期解的存在性.     

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.     

On Positive Periodic Solutions for Nonlinear Delayed Differential Equations

We prove the existence of positive ω-periodic solutions for the delayed differential equation

$$x^{\prime}(t) = a(t)g(x(t))x(t) - \lambda b(t)f(x(t - \tau (t))),$$

where λ is a positive parameter, \({a,b,\tau \in C(\mathbb{R},\mathbb{R})}\) are ω-periodic functions with \({a,b\geq 0,a,b \not \equiv 0,f,g\in C([0,\infty ),[0,\infty ))}\), g does not need to be bounded above or bounded away from 0, and g(0) = 0 is allowed.

     

广义时滞Hopfield型神经网络系统的平稳周期振荡

本文利用重合度理论和 V-泛函研究了一类具有周期输入的广义时滞 Hopfield型连续神经网络系统的平稳周期振荡问题 ,得到了其周期解存在、唯一和全局吸引的充分条件 .