零解

对于一类非线性系统零解的稳定性问题，本文采用线性类比法，将非线性系统形式转化为线性系统，构造出Liapunov函数，从而判定该非线性系统零解的稳定性。

For stability problem of null solution of a nonlinear system , firstly , this paper adopts linear analogy method to transform nonlinear systems into linear systems , and then constructs Liapunov functions , finally , proves the stability of null solution .

在E~n×（0，∞）上讨论双非线性抛物型方程ρ>λ>2的条件下，证明它的齐次Cauchy问题的非负整体解必是零解。

On En × ( 0 ,∞) consider the homogeneous Cauchy problem for a doubly nonlinear parabolic equation and prove its non-negative global solution must be a null solution . doubly nonlinear parabolic equation ; homogeneous Cauchy problem ;

n阶非线性微分方程组零解的稳定性

Stability for the zero solution of n-th order nonlinear differential system

一类n次系统零解的稳定性

The Stability of Zero Solution of a Kind of n Degree System

K拍振荡方程零解的稳定性

The stability of the equation of K stroke oscillations

用向量V函数法研究变系数线性时滞微分大系统零解的稳定性

The stability of large scale dynamical systems with delays by using vector V functions

一类受迫Liénard系统的最终零解

Eventually Vanished Solutions of a Forced Li é nard System

关于Hilbert空间中的多值凝聚映象方程的非零解

The existence of the nonzero solution for set-valued condensing mapping equation in Hilbert space

通过对一类n阶线性脉冲时滞微分方程零解稳定性的讨论，建立了零解稳定性的比较结果，给出了零解一致稳定、渐近稳定与指数稳定的充分条件。

The stability of a class of nth-order linear impulsive delay differential equations is studied and the comparison principle is established for the stability of the zero solution .

给出了神经网络BP学习算法与相应的微分动力系统解的存在性、唯一性定理和微分动力系统的零解稳定性定理。

For neural networks ' BP algorithm and their corresponding differential dynamics , the solution existence theorem , exclusiveness theorem and zero solution stability theorem of dynamic system are presented .

Hammerstein型积分方程非零解的存在性及应用

Nontrivial Solutions of Hammerstein Integral Equations with Applications

在不考虑阻尼且波浪频率、垂荡固有频率与纵摇固有频率满足一定关系时，零解会发生Hopf分岔。

Hopf bifurcations of zero solution are found when damping is ignored and the frequency of wave , frequency of heave and pitch satisfy certain relation .

利用Lyapunov方法讨论离散滞后广义系统，并给出了该类系统的零解一致稳定区域和渐近稳定区域的大小估计。

This paper discusses discrete_delay singular systems by using Lyapunov 's method and estimates the size of the uniformly stable region and asymptotic stability region around zero for discrete_delay singular systems .

在假设存在一个二次型控制Lyapunov函数的前提下，明确给出了使得这类系统的零解全局渐近稳定的反馈控制律。

Under the assumption that there exists a quadratic control Lyapunov function , a feedback control law was provided explicitly which renders the origin of this class of systems globally asymptotically stable .

通过引入具有齐次导数的时不变Lyapunov函数和近似系统的概念，给出一般非线性时变系统的零解渐近稳定的两个充分条件。

By introducing the concepts of time-invariant Lyapunov function with homogeneous derivative and the approximate system , two sufficient conditions for asymptotic stability of general nonlinear time-varying systems at the origin are obtained .

本文分别用参数变易法和V函数法，研究无穷时滞中立型方程零解的稳定性问题，获得了简洁、实用的稳定性充分准则。

In this paper , we use the variation of parameters method and V function method to study the stability of the zero solution of neutral differential equations with infinite delay . We got some simple sufficient conditions for stability .

首先利用Lyapunov方法定性、定量讨论了离散时滞与二次时滞广义系统并给出了零解一致稳定区域和渐近稳定区域的定量估计。

Firstly , it discusses qualitatively and quantitatively discrete system with delay and quadratic delay by Lyapunov 's method , and estimates the sizes of the uniform stability region and asymptotic stability region for the systems .

最后给出了Caputo分数阶积分微分系统零解的渐近稳定的结论。

Finally , the asymptotic solutions of the Caputo fractional Integral differential systems stability conclusions are given .

首先建立了两个重要的引理，然后再借助于逐段连续的Lyapunov函数，得到了脉冲微分系统的零解关于部分变元强稳定性的一些判定定理。

Effective sufficient conditions are found for strong stability with respect to partial variables of the zero solution of an impulsive differential system . The approach present is based on the specially introduced piecewise continuous Lyapunov functions and two important lemmas .

本文应用Banach压缩映射原理研究了一类非线性时滞微分方程的稳定性，建立系统零解渐近稳定的充分条件和必要条件，拓广并改进了已有的结果。

In this paper , we study the stability of a class of nonlinear delay differential equations via the Banach contractive mapping principle , and establish a sufficient condition and a necessary condition for the asymptotic stability of the system .

本文用向量Liapunov函数，向量及矩阵之范数，研究了更广一类的线性时变系统的零解稳定性问题。

In this paper , the asymptotic stability of zero solution about a class of linear time-varying systems is studied by using the norm of vector and matrix and vector Liapunov functions .

利用一般离散大系统零解稳定性的Lyapunov分解理论，结合区间矩阵的概念，讨论了线性灰色离散大系统和具有非线性扰动项的灰色离散大系统的稳定性问题，得到了若干稳定性的充分判据。

The stability of a linear and nonlinear gray discrete large-scale systems is studied in this paper , and some new algebraic criteria for the stability of trivial solutions are obtained by using Lyapunov 's decom - posed theorems and interval matrices .

本文利用Lyapunov方法对二次滞后离散奇异系统进行定性、定量分析并给出了该类系统的零解一致稳定吸引域和渐近稳定吸引域的定量估计。

This paper analyses in qualities and quantities the quadratic delay discrete singular systems by using Lyapunov 's method , and estimates quantitatively the uniformly stable attractive region and asymptotically stable attractive region around zero for the quadratic delay discrete singular systems .

研究非线性时滞系统的稳定性.应用Lyapunov函数，分别讨论确定性和不确定性非线性时滞系统.对于确定性系统，给出其零解渐近稳定的充分条件；

The stability of nonlinear systems with delay is studied . Using Lyapunov function , certain and uncertain nonlinear systems with delay are discussed , respectively . For the certain systems , the sufficient conditions for asymptotical stability of zero solution are presented .

根据Routh-Hurwitz判据，得到了零解的稳定区域，增大垂荡和纵摇的阻尼可减小不稳定区域。

According to Routh-Hurwitz criterion , the stability domain of zero solution is obtained and increasing heave or pitch damping can reduce the instability domain .

ΓaBpИloB对线性常微大系统建立了零解稳定性的独创判别准则[1][2]，改进他的结果，得到了变系数线性常微大系统零解稳定性的一些新的代数判据。

Γ aBPu Λ OB , advanced original criteria of the stability of Zero solution of large linear ordinary differential system . In this paper , his result is improved and some new algebraic criteria are obtained .

通过Liapunov泛函讨论有限时滞差分方程零解的稳定性以及解的有界性时，通常只是运用一个Liapunov泛函，这在构造上十分困难。

This paper considers the asymptotic stability of the zero solution and the boundedness of solutions for finite delay difference equations by Liapunov functional . Commonly only one Liapunov functional is used to resolve the problem , which is very difficult .

在常规渐近理论意义下关于GMM模型（Hansen，1982）的一个关键假设就是模型能被很好地识别，也就是矩条件在真值处有唯一的零解，具有满秩阶梯阵。

Under the conventional asymptotic theory in the GMM ( Hansen , 1982 ) model , a key assumption is identification ; i.e. the moment condition have a unique zero at the true value of parameter and have a full rank gradient .

在不假定非线性项非负的情况下，利用半序理论讨论了Hammerstein型积分方程非零解的存在性，并将所得结果应用于常微分方程两点边值问题。

In the case of not requiring the nonlinear terms non-positive , the existence of nontrivial solutions for the Hammerstein Integral Equations by using the partial ordering theory was discussed and some applications to ordinary differential equations with two-point bounded values .

层流边界层方程零解的稳定性分析

Analysis of the zero solution stability of laminar boundary layer equation