Hyers–Ulam stability of linear differential operator with constant coefficients

Let P(z) be a polynomial of degree n with complex coefficients and consider the n–th order linear differential operator P(D). We show that the equation P(D)f = 0 has the Hyers–Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

森林发展系统的一个非线性半离散模型

本文建立了森林发展系统的一类非线性林龄面积结构的半离散模型 ,并讨论了半离散系统解的存在唯一性 ,给出了线性半离散系统稳定的一些充分条件     

病毒感染群体动力学模型分析

本文构建并讨论了一类病毒感染的群体动力学模型,得到了模型存在轨道稳定周 期解的充分条件,较好地解释了在病毒持续感染者体内观察到的病毒载量波动现象.     

具有概周期系数的三种群第Ⅱ类功能性反应的全局渐近稳定性

讨论了一类具有概周期系数的三种群第Ⅱ类功能性反应的模型，通过利用微分不等式及构造适当的李雅普诺夫函数获得了其存在全局渐近稳定性的概周期解的充分条件．     

时滞差分方程的吸引性

本文给出了时滞差分方程x_n+1=x_nf(x_n,x_n-1),n=0,1,…解的全局吸引性的一个新的充分条件;作为应用,部分解决了G.Ladas的一个猜想.     

纬向对称准地转流的非线性稳定性定理

建立了周期域上准地转流在一般的边界条件下对应于Arnold第二定理的非线性稳定性定理。将扰动能量与扰动拟能的上界用初始扰动场的显示表示出来，从而建立了Liapunov意义下的非线性稳定性定理。     

迷宫密封不平衡转子动力系统的稳定性与分岔

研究迷宫密封对不平衡转子系统动力稳定性的影响.存在不平衡量的转子在旋转过程中受到周期激励,低转速时,转子作与激励同频率的周期运动,随着转速的提高,达到一定阈值时周期运动开始失稳.对迷宫密封的气动力采用Muszynska非线性力学模型,用打靶法求解转子运动周期解,并根据Floquet理论分析了周期解的稳定性及失稳后的动力学特性.     

树的稳定子集和稳定指标

一个实矩阵的符号稳定性问题在经济学、生态学等诸多领域中都有应用背景．本文利用[1]中给出的不可约矩阵的符号稳定性的有关结论，将一个实矩阵的符号稳定性判定问题转化为一个等价的图论问题，即判定无向树中一个点子集的稳定性问题．本文引入了树的稳定子集的概念并给出了稳定子集的递归判别方法．本文还提出井研究了树的稳定指标，即树中所有稳定子集的最小基数，证明了关于稳定指标的一个min—max型定理，井给出了n阶树的稳定指标的最好上界及达到上界的极树的完全刻划。     

ARMAX系统不外加输入激励的辨识

本文在不外加输入激励情况下，讨论了开环不稳定和非最小相位的ARMAX系统系数的一致估计．所用方法是用适应镇定的办法，使得闭环系统成为平稳可逆的ARMA过程，然后利用Yule-Walker方程给出闭环系统系数的一致估计，而把求开环系统系数的一致估计归结为解一组线性代数方程。     

Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type

We establish the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as a second-order, nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the location of the transonic shock which divides the two regions of smooth flow, and the equation is hyperbolic in the upstream region where the smooth perturbed flow is supersonic. We develop a nonlinear approach to deal with such a free boundary problem in order to solve the transonic shock problem. Our results indicate that there exists a unique solution of the free boundary problem such that the equation is always elliptic in the downstream region and the free boundary is smooth, provided that the hyperbolic phase is close to a uniform flow. We prove that the free boundary is stable under the steady perturbation of the hyperbolic phase. We also establish the existence and stability of multidimensional transonic shocks near spherical or circular transonic shocks.