周期二维Lotka—Volterra系统的一些新结果

该文研究周期二维Lotka－Volterra捕食食饵系统解的有界性，持续生存性以及正周期解的存在性和全局稳定性．并将结果推广到食饵有补充的周期二维Lotka－Volterra竞争系统上去，得到了一系列新的结果，改进和推广了文[1—3]的主要结论．     

周期Gompertz生态系统中的最优脉冲控制收获策略

以周期Gompertz系统为基础,讨论了周期变化的单种群生物资源的收获优化问题及种群的动力学性质.在单位收获努力量假设下,以最大可持续收获量为管理目标,确定了线性收获下的最优收获策略,获得了最优收获努力量、最大可持续收获及相应的最优种群水平的显示表达式,为自然资源的开发和利用提供了理论依据.     

一类具多偏差变元的p-Laplacian方程周期解的存在性

研究了一类具多偏差变元的p-Laplacian方程,为了得到该方程周期解的先验估计,运用分析技巧建立了一些新的不等式,进而利用Mawhin连续定理得到了这类方程周期解的存在性,得到了一些新的结果,推广和改进了已有结果.     

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。     

Weighted pseudo-almost periodic solutions to some differential equations

The paper considers some new classes of functions called weighted pseudo-almost periodic functions, which implement in a natural fashion the classical pseudo-almost periodic functions due to Zhang. Properties of these weighted pseudo-almost periodic functions are discussed, including a composition result for weighted pseudo-almost periodic functions. The results obtained are subsequently utilized to study the existence and uniqueness of a weighted pseudo-almost periodic solution to the heat equation with Dirichlet conditions.     

一类非线性泛函微分系统的概周期解

结合应用指数型二分性原理和Schaefer定理,考虑了一类完全非线性泛函微分方程概周期解的存在性问题,改善和推广了已有的结果.并将获得的结果推广到周期系统,获得了一些新的结果.     

Spreading speeds and traveling waves for periodic evolution systems

The theory of spreading speeds and traveling waves for monotone autonomous semiflows is extended to periodic semiflows in the monostable case. Then these abstract results are applied to a periodic system modeling man-environment-man epidemics, a periodic time-delayed and diffusive equation, and a periodic reaction-diffusion equation on a cylinder.     

普通型二分性与Favard定理

本文我们首先推广了著名的Ｆａｖａｒｄ定理并指出对齐次线性概周期系统由Ｆａｖａｒｄ定理所得到的概周期解是平凡的。然后利用推广后的Ｆａｖａｒｄ定理和普通型二分性讨论了一类线性和非线性系统的概周期解存在性。Ｎａｋａｊｉｍａ在文〔３〕中的结果是我们的结果的一种特殊情形。     

Periodic jordan rings and order structure

The aim of this paper is to obtain information about a periodic Jordan ring by using only properties of its idempotent elements. Osborn proves that a power-associative periodic ring having only one nonzero idempotent element is a division ring. so associative. He also proves that a periodic Jordan ring is a subdirect product of simple periodic Jordan rings and that a simple periodic Jordan ring is either a periodic field or a Jordan ring of capacity 2. Using these results we obtain some necessary and suficient conditions for a periodic Jordan ring to be associative, and these conditions are only given in terms of the idempotent elements. We also characterize the periodic Jordan ring which are a direct product of periodic fields and simple periodic Jordan rings of capacity two.     

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.     

拟线性系统周期边值问题

The existence and uniqueness results about quasilinear periodic boundary value problems are established by using the global inverse function theorem and the result about the existence and uniquencess of periodic solutions for the periodic boundary value problem of nonhomogeneous linear periodic system.     

Hopf bifurcation analysis in a one-dimensional Schnakenberg reaction-diffusion model

In this paper, we study the Hopf bifurcation phenomenon of a one-dimensional Schnakenberg reaction-diffusion model subject to the Neumann boundary condition. Our results reveal that both spatially homogeneous periodic solutions and spatially heterogeneous periodic solution exist. Moreover, we conclude that the spatially homogeneous periodic solutions are locally asymptotically stable and the spatially heterogeneous periodic solutions are unstable. In addition, we give specific examples to illustrate the phenomenon that coincides with our theoretical results.     

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。     

Periodic Solutions of a Model of Mitosis in Prog Eggs

In this paper,we discuss a simplified model of mitosis in frog eggs proposed by M.T. Borisuk and J.J. Tyson in [1]. By using rigorous qualitative analysis, we prove the existence of the periodic solutions on a large scale and present the space region of the periodic solutions and the parameter region coresponding to the periodic solution. We also present the space region and the parameter region where there are no periodic solutions. The results are in accordance with the numerical results in [1] up to the qualitative property.     

On the solutions of a second order nonlinear system with almost periodic forcing

A second order almost periodic perturbed nonlinear system with small parameter is discussed in this paper. Based on some analytical techniques and the method of averaging, some sufficient conditions are obtained for existence of one almost periodic solution. Also some suitable conditions are given for existence of two almost periodic solutions. The obtained new results generalized the known results in Seifert [1], [3] and He [2], [4]. Finally, some applications are presented to illustrate that our results are a good generalization of the known results.     

Dynamic behaviors of the periodic predator–prey system with distributed time delays and impulsive effect

In this paper, a periodic predator–prey system with distributed time delays and impulsive effect is investigated. By using the Floquet theory of linear periodic impulsive equation, some conditions for the linear stability of trivial periodic solution and semi-trivial periodic solutions are obtained. It is proved that the system can be permanent if all the trivial and semi-trivial periodic solutions are linearly unstable. We improve some results in Guo and Chen (2009) [1].     

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.     

On Wiener’s Theorem for functions periodic at infinity

We consider the functions periodic at infinity with values in a complex Banach space. The notions are introduced of the canonical and generalized Fourier series of a function periodic at infinity. We prove an analog of Wiener’s Theorem on absolutely convergent Fourier series for functions periodic at infinity whose Fourier series are summable with weight. The two criteria are given: for the function periodic at infinity to be the sum of a purely periodic function and a function vanishing at infinity and for a function to be periodic at infinity. The results of the article base on substantially use on spectral theory of isometric representations.     

Low-regularity solutions of the periodic general Degasperis-Procesi equation

This paper studies low-regularity solutions of the periodic general Degasperis-Procesi equation with an initial value. The existence and the uniqueness of solutions are proved. The results are illustrated by considering the periodic peakons of the periodic general Degasperis-Procesi equation.     

Nonexistence of periodic solutions and asymptotically periodic solutions for fractional differential equations

Using the final value theorem of Laplace transform, it is firstly shown that nonhomogeneous fractional Cauchy problem does not have nonzero periodic solution. Secondly, two basic existence and uniqueness results for asymptotically periodic solution of semilinear fractional Cauchy problem in an asymptotically periodic functions space. Furthermore, existence and uniqueness results are extended to a closed, nonempty and convex set which is a subset of a Fréchet space. Some examples are given to illustrate the results.