共查询到19条相似文献，搜索用时 46 毫秒
1.
考虑方程λ（１＋ｃｅ~（－τλ）＋ａ＋ｂｅ~（－τλ）＝０,（２）其中ａ,ｂ和ｃ为任意常数,τ为正常数,ｃ≠０．方程（１）为中立型方程 ｘ（ｔ）＋ｃｘ（ｔ－τ）＋ａｘ（ｔ）＋ｂｘ（ｔ－τ）＝０ （２）的特征方程．方程（１）为一常见的拟多项式方程．关于拟多项式函数, Ｐｏｎｔｒｙａｇｉｎ在 １９４２年给出了判断这类函数所有零点位于左半复平面的充要条件．但对中立型方程来说,由于这些条件往往难以验证,使得人们长期以来无法用Ｐｏｎｔｒｙａｐｉｎ定理找出方程（１）所有根具有负实部的充要条件．本文在克服了上述困难后,用Ｐｏｎｔｒｇｉｎ定理找出方程（１）所有根具有负实部的充要条件． 相似文献
2.
本文建立了方程ｘ（ｔ）＋ｃｔ（ｔ－ｔ）＋ａｘ（ｔ）＋ｂｘ（ｔ－ｔ）＝０零解渐近稳定的充要条件,给出了其零解渐近稳定的代数判据,同时纠正了文［２］中出现的错误． 相似文献
3.
本文建立了方程．．．．零解渐近稳定的充要条件,给出了其零解渐近稳定的代数判据,同时纠正了文（２）中出现的错误。 相似文献
4.
讨论了方程a2(x)(t-τ)+a1(x)(t-τ)+a0x(t-τ)+b2(x)(t)+b1(x)(t)+b0x(t)=δ的部分解. 相似文献
5.
考虑方程其中a，b为任意实常数,τ为正常数．本文在复数域上求得了方程（*）全部根的精确分布．在文[1]和[2]中应用Laplace变换法，得到了滞后型方程初值问题的形式解公式下：其中x（t）为初值问题的解，这里H（θ）为Heaviside函数．方程（*）为初值问题（E）中方程的特征方程．应用本文结果于形式解公式（1．1），可求得初值问题（E）的精确解．篇幅所限，此问题另文讨论． 相似文献
6.
讨论了方程 a2 x( t-τ) + a1x( t-τ) + a0 x( t-τ) + b2 x( t) + b1x( t) + b0 x( t) =δ的部分解 相似文献
7.
关于迭代方程 sum from i=1 to n λ_if~i(x)=F(x)可微解的讨论 总被引：2，自引：0，他引：2
本文作者讨论一般多项式形式的函数迭代方程,用现代分析的方法解决了其可微解的存在性、唯一性以及稳定性的问题. 相似文献
8.
葛渭高 《数学年刊B辑(英文版)》1993,(4)
本文对微分差分方程(t)=f(x(t-1))的简单周期解加以分类,通过证明周期解的对称性引理,给出了微分差分方程恰有 n+1个简单周期解的条件. 相似文献
9.
微分差分方程■(t)=f(x(t-1))简单周期解的个数 总被引：1，自引：0，他引：1
葛渭高 《数学年刊A辑(中文版)》1993,(4)
本文对微分差分方程■(t)=f(x(t-1))的简单周期解加以分类,通过证明周期解的对称性引理,给出了微分差分方程恰有n+1个简单周期解的条件。 相似文献
10.
本文研究了既具正系数又具负系数的一阶中立型微分方程ｄｄｔ［ｘ（ｔ）＋ｐｘ（ｔ－τ）－ｒｘ（ｔ－ρ）］＋ｑｘ（ｔ－ｓ）－ｈｘ（ｔ－ｖ）＝０其中ｐ,ｒ,τ,ρ,ｑ,ｈ,ｓ,ｖ都是正的常数,建立了一切解振动的带有若干个可调参数的一个充要条件和一系列充分性判据及某种形式的一个充要条件．有些充要条件和充分性判据包含或改进了前人的相应结果． 相似文献
11.
Sufficient conditions on the non-linearity are given which ensure that non-trivial solutions of second order differential equations of the form have a finite number of transverse zeros in a given finite time interval. We also obtain a priori lower bounds on the separation of zeros of solutions. In particular our results apply to non-Lipschitz non-linearities. Applications to non-linear porous medium equations are considered, yielding information on the existence and strict positivity of equilibrium solutions in some important classes of equations.
12.
In this paper, the distribution of zeros of solutions of the first-order neutral differential equation with a variable delayis studied. The estimate for the distance between adjacent zeros of the oscillatory solution of the above equation is obtained. 相似文献
13.
This paper discusses the problem of stability and periodic behaviour of linear planar difference systems appearing in modelling of discrete problems of population biology and Hopfield neural networks. We concentrate especially on procedures, which enable to formulate optimal (i.e. necessary and sufficient) conditions guaranteing such a behaviour. As a main tool, we analyse in detail location of zeros of characteristic polynomials with respect to the unit circle. From this viewpoint, derived results contribute also to the polynomial theory. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
14.
Kusano Takasi Manabu Naito 《Transactions of the American Mathematical Society》2002,354(12):4751-4767
In this paper the following half-linear ordinary differential equation is considered:
where 0$\"> is a constant, 0$\"> is a parameter, and is a continuous function on , 0$\">, and 0$\"> for . The main purpose is to show that precise information about the number of zeros can be drawn for some special type of solutions of (H such that
It is shown that, if and if (H is strongly nonoscillatory, then there exists a sequence such that , as ; and with has exactly zeros in the interval and ; and with has exactly zeros in and . For the proof of the theorem, we make use of the generalized Prüfer transformation, which consists of the generalized sine and cosine functions.
where 0$\"> is a constant, 0$\"> is a parameter, and is a continuous function on , 0$\">, and 0$\"> for . The main purpose is to show that precise information about the number of zeros can be drawn for some special type of solutions of (H such that
It is shown that, if and if (H is strongly nonoscillatory, then there exists a sequence such that , as ; and with has exactly zeros in the interval and ; and with has exactly zeros in and . For the proof of the theorem, we make use of the generalized Prüfer transformation, which consists of the generalized sine and cosine functions.
15.
D. B. Popovski 《BIT Numerical Mathematics》1981,21(1):129-130
King's two-step fifth-order methods for solving equations require two function and two derivative evaluations per iteration. Using exactly the same information and composing two-point methods of order 2.732 with themselves, other two-step methods can be obtained with asymptotic convergence rates 7.464 which is better than the 5 of King. 相似文献
16.
In this paper, a new class of fractional impulsive partial neutral stochastic integro-differential equations with infinite delay is introduced.Under some dissipative conditions, we obtain the existence, uniqueness and continuous dependence of mild solutions for these equations. An application involving a fractional stochastic parabolic system with not instantaneous impulses is considered. 相似文献
17.
We give a numerical criterion for a badly conditioned zero of a system of analytic equations to be part of a cluster of two zeros.
18.
T. Candan 《Mathematical Methods in the Applied Sciences》2015,38(7):1379-1392
The main goal of this article is to study the asymptotic properties and oscillation of the third‐order neutral differential equations with discrete and distributed delay. We give several theorems and related examples to illustrate the applicability of these theorems. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
19.
在α>1,且0<β<α情性下研究了高阶具非线性中立项不稳定型时滞微分方程[x(t)-pxα(t-τ)](n)=q(t)xβ(t-σ),(t≥t0)的振动和非振动性.利用一些新的技巧,获得了上述方程有界解振动的振动准则和至少存在一个非振动解的非振动准则,所得结果补充和推广了已有文献部分结果. 相似文献