一类微分方程边值问题解的唯一性

研究一个来源于研究退化抛物方程组的渐近性而产生的常微分方程组，证明了具紧支集解的唯一性。     

竞争扩散时滞模型的稳定性和Hopf分歧

本文研究一类含扩散的竞争时滞模型的定常解的稳定性以及Ｈｏｐｆ分坡解的存在性,进而给出分歧周期解的稳定性和分歧方向。     

时滞周期Logistic方程的周期解的稳定性

该文应用周期解的线性化稳定性的Ｆｌｏｑｕｅｔ理论研究了一类含时滞的周期Ｌｏｇｉｓｔｉｃ方程的周期解的稳定性．     

周期解的存在性和解的渐近性：含时滞的周期抛物系统

本文应用单调方法研究含时滞的周期抛物系统的周期解的存在性和解的渐近性,并应用所得结论讨论了一类含时滞的竞争－竞争－互惠生物模型。     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE HEAT EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

The purpose of this paper is to investigate the stability and asymptotic behav-ior of the time-dependent solutions to a linear parabolic equation with nonlinear boundarycondition in relation to their corresponding steady state solutions. Then, the above resultsare extended to a semilinear parabolic equation with nonlinear boundary condition by an-alyzing the corresponding eigenvalue problem and using the method of upper and lowersolutions.     

竞争扩散方程一类行波解的存在性与波速估计

本文研究了反应扩散系统．我们用打靶法及关于ＫＰＰ方程的有关结果，得到了行波解的存在性并给出了波速估计．     

竞争扩散燃烧网络的渐近状态

本文研究了竞争扩散燃烧网络问题,将其转换成反应扩散系统的初边值问题,建立了有关单个方程及方程组的“门槛”(threshold)结果及hair trigger性质,并用这些结果到了竞争扩散燃烧网络渐近状态的较精确分析。     

A CONDITION OF THE EXISTENCE OF STABLE POSITIVE STEADY-STATE SOLUTIONS FOR A ONE PREDATOR TWO PREY SYSTEM

One predator two prey system is a research topic which has both the theoretical and practical values.This paper provides a natural condition of the existence of stable pcsitive steady-state solutions for the one predator two prey system.Under this conditon we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem,discuss the positive stable solution problem bifureated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.     

THE BIFURCATION ANALYSIS OF EXISTENCE AND TABILITY OF POSITIVE STEADY-STATE SOLUTION FOR A ONE-PREDATOR-TWO-PREY SYSTEM

This paper discusses the existence and stability of steady-states for a three-dimensional system ef parabolic partial differential equations subject to Dirichlet boundary conditions, i.e. the situation in which a predator feeds on twoprey species. Resultts are obtained by the use of spectral analysis and bifurcation theory.     

架空电线振动理论分析

本文研究水平风力作用在架空电线上引起架空电线垂直振动的问题。 架空电线振动,使线股疲劳,在悬挂点处造成折断,是高压输电线路设计和运行中的一个重大问题。 风吹电线,可以看成是空气绕圆柱体流动,根据卡尔曼涡列的有关结论与本文中引证的一个环量不变定理,证明了圆柱面上存在着周期变化的环量,利用带环量圆柱绕流的儒可夫斯基公式,即可计算在电线上的周期垂直力。 架空电线振动的数学模型是弦振动方程的混合问题,我们弄清了风对架空电线的作用之后,讨论了强迫振动及共振等问题。 本文所得的架空电线强迫振动频率、振幅及振动过程与实际观测的情况相吻合。所用的论点和方法,对于研究烟囱、架空管道等建筑设施的弹性振动也有参考意义。