非线性中立双曲型泛函微分方程解的振动判据

讨论一类多滞量非线性中立双曲型泛函微分方程解的振动性质，获得了其一切解振动的充分条件；指出了与普通双曲型偏微分方程质的差异。     

高阶泛函偏微分程边值问题的强迫振动

本文研究一类高阶泛函偏微分方程边值问题的强迫振动性．主要工具是平均技巧，利用它将问题归结于相应的泛函微分不等式的振动性的研究．     

中立型向量双曲偏微分方程的H-振动性

本文研究了一类中立型向量双曲偏微分方程边值问题的振动性.利用Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维泛函微分不等式正解的不存在性问题,获得了该类边值问题在Dirichlet边界条件下所有解H-振动的若干新的充分条件,其中H是Rm中的单位向量.     

高阶非线性阻尼脉冲微分方程解的振动性

研究了一类高阶非线性阻尼脉冲微分方程振动状态,得到振动解的充分条件.     

OSCILLATORY BEHAVIOR OF EVEN ORDER MIXED NEUTRAL DIFFERENTIAL EQUATIONS

In this paper,we shall consider a class of even order mixed neutral differential equations. Some new oscillations criteria of the solutions are obtained.     

OSCILLATION OF DIFFERENTIAL EQUATION ON CYLINDRICAL SURFACE

1IntroductionWhenthebehaviorofdynamicalautonomoussysterllislrlapedontothephasespace,weaskthatabeha,viorofsystemafldapointofthephasespa(fetobemutualone-to-Onecontinuouscorrespondence.FOrthenon-autonomoussystemweaskthatabehaviorofsystemtocorrespondwithonlyo…     

自治时滞微分方程的线性化振动性

研究了非线性时滞微分方程的线性化振动性。     

非线性中立抛物型泛函微分方程解的振动判据

讨论一类多滞量中立抛物型泛函微分方程解的振动性质,获得了其一切解振动的充分条件及线性情况下的充要条件;指出了与普通抛物型偏微分方程质的差异。     

《非线性连续分布偏差变元微分方程的线性化振动性》一文的注记

本文主要指出[1]关于时滞微分方程线性化振动的几个定理的错误。     

中立抛物型偏微分方程解的强迫振动

本文讨论一类多滞量中立抛物型偏微分方程解的振动性质 ,获得了其一切解振动的充分条件 ;指出了与普通抛物型偏微分方程质的差异 .     

带强迫项的脉冲时滞微分方程的振动性

研究带一阶强迫项的脉冲时滞微分方程的振动性,借助于Kartsatos变换,得到了若干判别这类方程振动的充分性条件,所得的结果推广并改进了时滞微分方程振动性理论中某些已知的相关结果。     

On the Oscillation of the Fourth Order Differential Equations

61.IntroductionWeconsiderthefourthorderdifferentialequationx(`)(t)-p(t)lx(t)I'sgnx(t)=O,(1.l)wherea>l,isconstant,andp(t)ispositivecontinuousfunctionon[t,,oo),to>o.Werestrictourattentiontothosenontrivialsolutionsx(t)of(1.1)whichexistonsomehalf-[ine[T:,co)cy[t,,oo),suchasolutioniscalledapropersolutionof(1.l).ApropersolutioniscalledoscillatoryifithasarbitrarilylargezerosFotherwiseitiscallednonoscillatory.Wecon-sidertheoscillationandnonoscillationofpropersolutionsof(l,l).WeletEdenotethesetofall…     

非线性中立抛物型时滞偏微分方程解的振动性质

讨论一类多滞量非线性中立抛物型时滞偏微分方程解的振动性质 ,应用积分不等式和泛函微分方程的某些结果 ,在第一类边界条件下获得了其一切解振动的一系列充分条件 .结论充分表明了时滞量的决定性作用 ,指出了其与普通抛物型偏微分方程质的差异 .     

Preservation of Oscillations in the Runge-Kutta Method for a Type of Advanced Differential Equation

This article is concerned with the preservation of oscillations for differential equations with piecewise constant arguments of advanced type. By using the Runge-Kutta method, new oscillation conditions for numerical solution are established. We prove that oscillations of the analytic solution are preserved by the numerical solution in the Runge-Kutta method under some conditions. Some experiments are given.     

Center projections for smooth difference equations of mixed type

We study a class of mixed type difference equations that enjoy a special smoothening property, in the sense that solutions automatically satisfy an associated functional differential equation of mixed type. Using this connection, a finite dimensional center manifold is constructed that captures all solutions that remain sufficiently close to an equilibrium. The results enable a rigorous analysis of a recently developed model in economic theory, that exhibits periodic oscillations in the interest rates of a simple economy of overlapping generations.     

OSCILLATION OF IMPULSIVE HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION WITH DELAY

In this paper, oscillation properties of the solutions of impulsive hyperbolic equation with delay are investigated via the method of differential inequalities. Sufficient conditions for oscillations of the solutions are established.     

非线性中立双曲型时滞偏微分方程解的振动性质

讨论一类多滞量非线性中立双曲型时滞偏微分方程解的振动性质,应用积分不等式和泛函微分方程的某些结果,获得了其一切解振动的一系列充分条件。结论充分表明了时滞量的决定性作用,指出了其与普通双曲型偏微分方程质的差异。     

无限滞后测度泛函微分方程的平均化

本文研究了无限滞后测度泛函微分方程的平均化.利用广义常微分方程的平均化方法,在无限滞后测度泛函微分方程可以转化为广义常微分方程的基础上,获得了这类方程的周期和非周期平均化定理,推广了一些相关的结果.     

NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATIONS OF PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH DELAY

In this paper, by making use of the integral method and some results of the functional differential equations, oscillatory properties of the solutions of certain parabolic partial differential equations with multi-delays are investigated and a series of necessary and sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by the delay and hence reveal the varied difference between these equations and those without delay.     

Oscillatory behaviour in functional differential systems of neutral type

In this paper are obtained several criteria for oscillations of a class of autonomous functional differential systems of neutral type.