Periodic Solutions of Schrǒdinger Flow from S^3 to S^2

Abstract This paper deals with the periodic solutions of Schr?dinger flow from S ³ to S ². It is shown that the periodic solution is related to the variation of some functional and there exist S1-invariant critical points to this functional. The proof makes use of the Principle of Symmetric Criticality of Palais. *Project supported by the National Natural Science Foundation of China (No.10321001).     

Periodic Duffing delay equations with state dependent impulses

Conditions are obtained for the Duffing equation with delay and state dependent impulses to admit a periodic solution.     

区间上单峰扩张自映射周期轨道的超旋转对

设f是区间I=[0,1]上的单峰扩张自映射, k ∈N,m≥2,λm,k是方程x(k-1)m(xm- 1)Q(x,m 1) (x(k-1)m-1)Q(x,m)=0在(1, ∞)上的唯一实根,其中Q(x,m)=(xm- 2xm-1 1).本文证明:若f的扩张常数λ≥λm,k,则f有超旋转对为(k,km 1)的周期轨道. 此外,还指出,当1<λ<λm,k时,在区间上存在单峰扩张自映射具有扩张常数λ却无超旋转对为(k,km 1)的周期轨道.     

双函数法及一类非线性发展方程的精确行波解

给出一种求解非线性发展方程精确行波解的新方法：双函数法。使用此方法，获得了一类非线性发展方程的许多精确行波解，其中包括孤波解和周期解，推广了文献用其它方法取得的结果，同时还获得了许多新的弧波解和周期解，借助于Mathemat-ica，此方法能部分地在计算机上实现。     

A Functional Non-Central Limit Theorem for Jump-Diffusions with Periodic Coefficients Driven by Stable Lévy-Noise

We prove a functional non-central limit theorem for jump-diffusions with periodic coefficients driven by stable Lévy-processes with stability index α>1. The limit process turns out to be an α-stable Lévy process with an averaged jump-measure. Unlike in the situation where the diffusion is driven by Brownian motion, there is no drift related enhancement of diffusivity.     

脉冲中立型单种群模型的正周期解

利用拓扑度理论讨论了一类具有脉冲的中立型单种群生态模型,得到了该系统的正周期解存在的充分条件.     

Multiplicity of positive periodic solutions to superlinear repulsive singular equations

In this paper, we study positive periodic solutions to the repulsive singular perturbations of the Hill equations. It is proved that such a perturbation problem has at least two positive periodic solutions when the anti-maximum principle holds for the Hill operator and the perturbation is superlinear at infinity. The proof relies on a nonlinear alternative of Leray-Schauder type and on Krasnoselskii fixed point theorem on compression and expansion of cones.     

On the dynamics of nonautonomous periodic general dynamical systems and differential inclusions

We establish the existence and stability results for periodic nonautonomous uniform forward attractors of periodic general dynamical systems (set-valued dynamical systems). We also investigate the dynamical behavior of nonautonomous periodic differential inclusion x^′(t)∈f(t,x(t)) on R^m with only upper semi-continuous right-hand side by applying the abstract results. Firstly, we show that if the system has a compact uniformly attracting set, then it has a periodic nonautonomous uniform forward attractor A. Secondly, we prove that A is robust with respect to both internal and external perturbations. Finally, we apply the robustness result to discuss the effects of small time delays to asymptotic stability of the system.     

Quasisolutions and dynamics of time-periodic nonquasimonotone reaction-diffusion systems

In this paper, using the upper-lower solution method, we investigate the properties of periodic quasisolutions for time-periodic nonquasimonotone reaction-diffusion systems, and present some existence, asymptotic behavior results for two ecological models.