OSCILLATION RESULTS RELATED TO INTEGRAL AVERAGING TECHNIQUE FOR EVEN ORDER NEUTRAL DIFFERENTIAL EQUATION WITH DEVIATING ARGUMENTS

In this paper, we study an even order neutral differential equation with deviating arguments, and obtain new oscillation results without the assumptions which were required for related results given before. Our results extend and improve many known oscillation criteria, based on the standard integral averaging technique.

OSCILLATION CRITERIA FOR CERTAIN EVEN ORDER NEUTRAL DIFFERENTIAL EQUATIONS

Using the generalized Riccati technique and the averaging technique, we establish several oscillation criteria for certain even order neutral differential equation. The results obtained in this paper extend and improve some known results in the previous literatures.

OSCILLATION FOR NEUTRAL DELAY DIFFERENTIAL EQUATION WITH POSITIVE AND NEGATIVE COEFFICIENTS

In this paper, a new oscillating result is established for the first order neutral delay differential equation with positive and negative coefficients, which improves and generalizes several results in the literatures.

OSCILLATIONS OF SOLUTIONS OF NEUTRAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS AND DELAYS

Consider the neutral differential equations with variable coefficients and delays [x(t)-p(t)x(t-r(t))]'+ Qj(t)x(t-σj(t))=0. (1)We establish sufficient conditions for the oscillation of equation (1). Our condition is 'sharp' in the sense that when all the coefficients and delays of the equation are constants.Our conclusions improve and generalize some known results.

OSCILLATION AND EXISTENCE OF POSITIVE SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH POSITIVE,NEGATIVE COEFFICIENTS

This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The 'sharp' conditions of oscillation for the equation have been obtained, i.e., the conditions are sufficient and necessary when all of the coefficients are constants. These conditions are distinguished from the previous criteria in the literatures, and also weaker than those existing results.

OSCILLATION CRITERIA FOR A CLASS OF FIRST-ORDER NEUTRAL PANTOGRAPH DIFFERENTIAL EQUATIONS OF EULER TYPE

In this paper, we further investigate a class of first order neutral Pantograph differential equations of Euler type by Guan and Shen . Some infinite-integral conditions for the oscillation of all solutions are established.

OSCILLATORY PROPERTY OF SOLUTIONS FOR SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATION TO BE CHANGED INTO AN "INTEGRALLY SMALL" COEFFICIENT

Oscillatory property of solutions of the second order differential equation with an "integrally small" coefficient were studied in Refs. [1, 2], in which the corresponding results were improved in [3], but we have not yet seen any oscillation result about the second order functional differential equation with an "integrally small" coefficient. The aim of this note is to show some oscillatory theorems.We consider the following second order functional differential

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF SECOND ORDER NONLINEAR ELLIPTIC DIFFERENTIAL EQUATIONS

In this paper, the second order nonlinear elliptic differential equations (E) (n)Sigma (i,j=1) partial derivative/partial derivativex(j)[a(i,j)(x,y) partial derivative/partial derivativex(j)y] + q(x)f(y) = e(x) are considered in an exterior Omega subset of R-n, where q(x) is allowed to change sign. Some sufficient conditions for any solutions y(x) of (E) to be satisfied liminf\\x\--> infinity \y(x)\ = 0 are obtained. Particularly, these results improve the previous results for second order ordinary differential equations.

一类时变偶阶微分方程的Philos型准则

振荡理论是微分方程领域的一个重要分支,在物理学和数学中起着基础性作用。尽管微分方程振荡行为的研究已经取得了许多成果,但是关于同时包含非线性中性项、阻尼项、不同符号系数和多变量延迟的非线性偶阶微分方程的研究相对较少,为此重点研究了具有上述特征的非线性偶阶微分方程的振荡行为,并得出一些相关结论。

具拟线性扩散系数的脉冲中立型抛物系统的(强)振动性

研究一类具拟线性扩散系数的脉冲中立型抛物偏微分系统解的(强)振动性,直接利用振动的定义、Green公式和Neumann边值条件将这类脉冲中立型抛物系统的振动问题转化为脉冲中立型微分不等式不存在最终正解的问题,并利用最终正解的定义和脉冲中立型微分不等式,获得了该类系统(强)振动的充分判据.所得结果充分反映了脉冲和时滞在振动中的作用。

一类二阶中立型微分方程的振动和非振动准则

中立型泛函微分方程的振动性在理论和应用中有着重要意义.研究了一类具有正负系数的二阶非线性中立型时滞泛函微分方程的振动性,利用Banach空间的不动点原理,通过引入参数函数并结合一些分析技巧,获得了该类方程存在非振动解的新的准则,并同时得到了该类方程振动的判别准则,这些准则改善了对方程的条件限制,所得结论推广并改进了现有文献中的一系列结果.

具正负系数的二阶阻尼微分方程的振动性

研究了一类具有正负系数的二阶非线性变时滞中立型阻尼泛函微分方程的振动性,通过引入参数函数和Riccati变换,获得了该类方程振动的判别准则,这些准则改善了对方程的条件限制,所得结论推广并改进了现有文献中的一系列结果,并给出了例子用以说明本文的主要结论。

一类多时滞二阶中立型微分方程的振动性

中立型泛函微分方程的振动性在理论和应用中有着重要意义.研究了一类具有正负系数的二阶非线性中立型时滞泛函微分方程的振动性,利用Banach空间的不动点原理,通过引入参数函数并结合一些分析技巧,获得了该类方程存在非振动解的新的准则,并得到了该类方程振动的判别准则,这些准则改善了对方程的条件限制,所得结论推广并改进了现有文献中的一系列结果.

一阶中立型时滞微分方程的强迫振动

该文建立了一类带有正负系数的强迫一阶中立型时滞微分方程的有界解振动或者渐近趋向于零的若干新的充分条件．

椭圆型微分方程振动性的函数序列方法

在Ｒｎ 的一个外区域Ω上考虑二阶非线性椭圆型微分方程∑ｎｉ，ｊ＝１ｘｉＡｉｊ（ｘ，ｙ）） ｘｊｙ ＋ｐ（ｘ）ｆ（ｙ） ＝ ０ 解的振动性质（ 其中ｎ ≥２，ｐ（ｘ） 可变号） ． 借助于函数序列方法并利用基本不等式技巧，

具正负系数中立型微分方程解的振动性

本文考虑具有正负系数中立型方程［ｙ（ｔ）－Ｒ（ｔ）ｙ（ｔ－ｒ）］＇＋Ｐ（ｔ）ｙ（ｔ－τ）－Ｑ（ｔ）ｙ（ｔ－σ）＝０，其中Ｐ，Ｑ，Ｒ∈Ｃ（［ｔ０，∞），Ｒ＋），ｒ∈Ｅ（０，∞），τ，σ∈［０，∞］。通过减弱条件~［１～８］：∫_（ｔ_０）~∞［Ｐ（ｓ）－Ｑ（ｓ－τ＋σ）］ｄｓ＝∞获得了方程所有解振动的新的充分条件。

Euler方程的解与二阶微分方程的振动性

给出了一般Euler方程的解并讨论它的振动性,利用这些结果和Sturm比较理论研究了二阶微分方程的振动性质.对于一类具有"积分小"系数或可化为具有"积分小"系数的二阶微分方程的振动性与非振动性给出了简便、精确的判别方法.

一阶中立型微分方程解的振动性(英文)

给出了关于一阶中立型正负系数微分方程解的振动性的新的充分条件.

具有正负系数的二阶中立型方程的振动性定理

利用Banach空间的不动点原理,通过引入参数函数和Riccati变换,获得了该类方程存在非振动解的新的准则,并同时得到了该类方程振动的判别准则,这些准则改善了对方程的条件限制,所得结论推广并改进了现有文献中的一系列结果.

具有正负系数的二阶非线性中立型方程的非振动准则

中立型泛函微分方程的振动性在理论和应用中有着重要意义。本文研究了一类具有正负系数的二阶非线性中立型时滞泛函微分方程的振动性,利用Banach空间的压缩映象原理和一些分析技巧,建立了该方程非振动的一些新的准则,并给出了定理应用的例子。所得结论推广和改进了现有文献中的一系列结果。