一类含时滞的反应扩散方程的周期解和概周期解

本文研究一类含时滞的反应扩散方程和方程组.应用单调方法得到了这类方程存在周期解和概周期解一些充分条件.     

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。     

非单调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、下解方法及不动点理论,研究了一类反应项不具任何单调性的时滞反应扩散方程,证明了此方程对应的边值问题存在唯一的周期(或概周期)解.并通过一个经典的化学模型说明了所得结果的意义.     

一个具有非局部效应的非线性周期反应扩散方程的渐近形态

研究一个具有非线性-非局部反应的周期反应扩散系统.利用周期半流的渐近理论来讨论渐近波速c~*和周期行波解的存在性,证明参数c~*也是周期行波解的最小波速,并清晰描述解传播的阈值性质.最后给出渐近波速和最小波速c~*的估计.     

一类非线性方程的行波解分支

运用平面动力系统的分支方法,研究了一类非线性方程的行波解,画出了在不同参数条件下的相图,证明方程存在周期行波解和周期尖波解.给出了有界波的精确的参数表达式,指出了周期尖波是周期波的极限形式,同时指出了方程不存在圈孤子解.     

一类具非线性功能反应和捕获的捕食食饵系统周期解的全局存在性

通过利用Mawhin重合度理论讨了一类具有非线性功能反应和捕获的捕食食饵系统的全局周期解的存在性,得到了周期解存在的充分条件.     

一类具有时滞功能反应的两种群捕食-食饵脉冲扩散系统的周期解

本文研究了一类具有脉冲的时滞功能反应的两种群捕食-食饵扩散模型的周期解存在性问题.应用重合度理论方法和不等式的分析理论,得到该系统正周期解存在的充分条件.     

时滞反应扩散方程——单调方法与有界解、周期解、概周期解的存在性

在本文中,我们利用变形的单调方法在一般的条件下证明了一类含时滞的反应扩散方程组的周期解和概周期解的存在性与唯一性,这类结果,目前在有关文献中还比较少见。     

一类具有Beddington-DeAngelis功能反应的空气污染周期动力学模型的正周期解的存在性

利用重合度理论中的延拓定理,研究了一类具有Beddington-DeAngelis功能反应的空气污染周期动力学模型的正周期解的存在性,得到了该模型存在正周期解的充分条件.     

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.     

Existence of Non-trivial Nonnegative Periodic Solutions for a Nonlinear Diffusion System

In this paper, by the method of upper and lower solutions, we establish the existence of the non-trivial nonnegative periodic solutions for a class of degenerate diffusion system arising from dynamics of biological groups.     

一类非线性扩散系统非平凡非负周期解的存在性

In this paper,by the method of upper and lower solutions,we establish the existence of the non-trivial nonnegative periodic solutions for a class of degenerate diffusion system arising from dynamics of biological groups.     

Existence and multiplicity results of positive doubly periodic solutions for nonlinear telegraph system

In this paper, the existence of positive doubly periodic solutions for nonlinear telegraph system is discussed using the method of upper and lower solutions.     

Explicit exact periodic wave solutions and their limit forms for a long waves-short waves model

A long waves-short waves model is studied by using the approach of dynamical systems. The sufficient conditions to guarantee the existence of solitary wave, kink and anti-kink waves, and periodic wave in different regions of the parametric space are given. All possible explicit exact parametric representations of above traveling waves are presented. When the energy of Hamiltonian system corresponding to this model varies, we also show the convergence of the periodic wave solutions, such as the periodic wave solutions converge to the solitary wave solutions, kink and anti-kink wave solutions, and periodic wave solutions, respectively.     

概周期系统概周期解的存在唯一性

运用Ｌｉａｐｕｎｏｖ函数，研究了概周期系统概周期解的存在唯一性，得到了一个方便应用的判定定理．     

Approximate periodic solutions of a nonlinear parabolic system and an identification problem

This work continues our study in [L. Lei, Identification of parameters through the approximate periodic solutions of a linear parabolic system, preprint, 2005] on the identification problem for the coefficients for the lower order terms in a parabolic system, through its approximate periodic solutions. Different from the work in [L. Lei, Identification of parameters through the approximate periodic solutions of a linear parabolic system, preprint, 2005], our system now is nonlinear and the coefficients to be detected are from the first order term. From the application point of view, we now try to determine the diffusion coefficients for the system by the observation over a subregion of the physical domain. The existence and uniqueness problem of the approximate periodic solutions is studied in the first part of the paper.     

Exact solutions and dynamics of the Raman soliton model in nanoscale optical waveguides, with metamaterials, having parabolic law non-linearity

This paper investigate the Raman soliton model in nanoscale optical waveguides, with metamaterials, having parabolic law non-linearity by using the method of dynamical systems. The functions $q(x,t)=\phi(\xi)\exp(i(-kx+\omega t))$ are solutions of the equation (1.1) that governs the propagation of Raman solitons through optical metamaterials, where $\xi=x-vt$ and $\phi(\xi)$ in the solutions satisfy a singular planar dynamical system (1.5) which has two singular straight lines. By using the bifurcation theory method of dynamical systems to the equation of $\phi(\xi)$, bifurcations of phase portraits for this dynamical system are obtained under 28 different parameter conditions. Based on those phase portraits, 62 exact solutions of system (1.5) including periodic solutions, heteroclinic and homoclinic solutions, periodic peakons and peakons as well as compacton solutions are derived.