一类具时滞高阶Rayleigh方程的周期解的先验界性

本文首先建立了一类具时滞高阶Bayleigh方程的周期解的先验有界性．进而，借助这些有界性，并利用Mawhin连续定理获得了周期解的存在性定理．     

一类离散时滞具一般功能性反应的捕食——食饵系统的周期解

研究了一类离散时滞具一般功能性反应的捕食-食饵系统,运用重合度理论中的延拓定理得到了系统至少存在一个正的周期解的充分条件.特别地,周期解的上界和下界也是确立的.     

一类具偏差变元Rayleigh方程周期解的存在性

作者研究一类具偏差变元Ralyleigh方程周期解的存在性问题,利用重合度拓展定理得到了周期解存在性结论.有意义的是本文周期解先验界估计的方法与已有的工作均不相同.     

Existence of periodic solutions for a class of second order differential equation with deviating argument

By means of Mawhin’s continuation theorem, a second order differential equation with a deviating argument is studied. A new result on the existence of periodic solutions is obtained. Meanwhile, the approaches used to estimate a priori bounds of periodic solutions are different from the corresponding ones in the known literature.     

一类非线性项前系数可变号的高阶Duffing方程的周期解存在性问题

利用Fourier级数理论,伯努利数理论和重合度理论研究了一类具偏差变元的高阶泛函微分方程$x^{(m)}(t)+\beta (t)g(x(t-\tau(t)))=p(t)$的周期解问题,得到了周期解存在性的新结论,有意义的是非线性项前的系数$\beta(t)$可变号,但是,周期解先验界估计方法与已有工作不同.     

Periodic solutions in periodic state-dependent delay equations and population models

Sufficient and realistic conditions are obtained for the existence of positive periodic solutions in periodic equations with state-dependent delay. The method involves the application of the coincidence degree theorem and estimations of uniform upper bounds on solutions. Applications of these results to some population models are presented. These application results indicate that seasonal effects on population models often lead to synchronous solutions. In addition, we may conclude that when both seasonality and time delay are present and deserve consideration, the seasonality is often the generating force for the often observed oscillatory behavior in population densities.

     

Multiple periodic solutions of delayed predator–prey systems with type IV functional responses

In this paper, we considered a periodic predator–prey system with a type IV functional response, which incorporates the periodicity of the environment. Sufficient conditions for the existence of multiple positive periodic solutions are established by applying the continuation theorem. This is the first time that multiple periodic solutions are obtained by using the theory of coincidence degree. Moreover, unlike other types of functional responses, a type IV functional response declines at high prey densities. Thus the existing arguments for obtaining bounds of solutions to the operator equation Lx=λNx are inapplicable to our case and some new arguments are employed for the first time.     

一类多偏差变元的n种群Lotka-Volterra模型的周期正解

本文研究了一类多偏差变元Lotka-Volterra种群模型的间期正解问题,利用重合度拓展定理和一些分析技巧,得到了周期正解存在性的新结果.与已有文献相比,本文所讨论的模型更具一般性,它包含了以前人们所研究的竞争-种群模型、捕食-种群模型等,而且估计先验界的方法也是全新的.     

PERIODIC SOLUTIONS OF A CLASS OF EVEN ORDER DIFFERENTIAL EQUATIONS

1Introduction1.1Theal1TIof'1.hispa;pel'istopl'ovidesufficientcon(lit,iolls1'or1.lieexisted(feofperiodicsolutjoilsof1,he21't,horderdift'erentitxleqllal,ionandthellorl--cxistcnceoflloTI--ti}ivialperio相似文献   

Jorke's Theorem and Wirtinger's Inequality

We consider autonomous systems of ordinary differential equations (of first or higher order) whose right-hand sides satisfy the Lipschitz condition stated in terms of the Euclidean metric and of nonnegative matrices. Using Wirtinger's inequality, we prove theorems on the lower bounds for the periods of periodic nonstationary solutions of autonomous systems, which generalize Jorke's theorem. In the case of nonnegative indecomposable matrices we discuss the sharpness of the estimates obtained.     

一类泛函微分方程半正问题的正周期解

运用Krasnosel’skii不动点理论研究了一类含参泛函微分方程半正问题正周期解的存在性．获得了当参数充分小时正周期解的存在性结果以及半正问题正周期解存在的充分条件．丰富了一阶泛函微分方程解的存在性理论．     

EXISTENCE OF PERIODIC SOLUTIONS OF A CLASS OF SECOND-ORDER NON-AUTONOMOUS SYSTEMS

In this paper, we are concerned with the existence of periodic solutions of second-order non-autonomous systems. By applying the Schauder''s fixed point theorem and Miranda''s theorem, a new existence result of periodic solutions is established.     

Periodic solutions for a type of neutral system with variable parameters

In this paper, we firstly analyze some properties of the linear difference operator $[Ax](t)=x(t)-C(t)x(t-\tau),$ where $C(t)$ is a $n\times n$ matrix function, and then using Mawhin''s continuation theorem, a first-order neutral functional differential system is studied. Some new results on the existence and stability of periodic solutions are obtained. The results are related to the deviating arguments $\tau$ and $\mu$. Meanwhile, the approaches to estimate a $prior$ bounds of periodic solutions are different from the corresponding ones of the known literature.     

Boundary-value problems for differential equations unsolvable with respect to the higher time derivative

For differential equations with constant coefficients unsolvable with respect to the higher time derivative, we establish conditions of the existence and uniqueness of solutions of problems with conditions local in time and periodic in space variables. We prove a metric theorem on lower bounds of small denominators appearing in the construction of solutions of the problems.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 9, pp. 1197–1208, September, 1995.This work was supported by the Foundation for Fundamental Research of the Ukrainian State Committee on Science and Technology.     

A note on periodic solutions of nonautonomous second-order systems

A multiplicity theorem is obtained for periodic solutions of nonautonomous second-order systems with partially periodic potentials by the minimax methods.

     

A priori bounds for periodic solutions of a Duffing equation

In this paper a well known Duffing type equation is considered. By means of a Liapunov function and careful estimation, we establish a priori bounds for periodic solutions and their derived functions. Coincidence theorems can then be applied to yield sufficient conditions for the existence of periodic solutions. Our conclusion improve several well known results in the literature.     

一类中立型泛函微分系统周期解存在性问题

首先对线性差分算子M:[Mx](t)=z(t)-Cx(t-r)的性质进行了研究,在此基础上利用Mawhin重合度拓展定理研究了一类具偏差变元的中立型泛函微分系统的周期解问题,得到了周期解存在性的新结论.本文的矩阵C仅为一般的实方阵,不必为实对称阵,因而结果改进和推广了已有工作.此外,本文周期解先验界估计方法与已有工作也不相同.     

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.     

EXISTENCE OF MULTIPLE POSITIVE PERIODIC SOLUTIONS TO A CLASS OF INTEGRO-DIFFERENTIAL EQUATION

In this paper,by the Avery-Henderson fixed point theorem,we investigate the existence of multiple positive periodic solutions to a class of integro-differential equation. Some suficient conditions are obtained for the existence of multiple positive periodic solutions.     

一类无穷时滞周期Lotka-Volterra型系统的正周期解

该文研究一类无穷时滞周期Ｌｏｔｋａ Ｖｏｌｔｅｒｒａ型系统正周期解的存在性．应用Ｓｃｈａｕｄｅｒ不动 点定理得到了一个比较一般的正周期解存在定理．文献［１,２］中的主要结果被改进和推广．