OSCILLATION CRITERIA FOR FORCED SUPERLINEAR DIFFERENCE EQUATIONS

Using Riccati transformation techniques,some oscillation criteria for the forced second-order superlinear difference equations are established.These criteria are dis- crete analogues of the criteria for differential equations proposed by Yan.     

GENERALIZED RICCATI TRANSFORMATION AND OSCILLATION FOR LINEAR DIFFERENTIAL EQUATIONS WITH DAMPING

Using generalized Riccati transformation, some new oscillation criteria for damped linear differential equations are established. These results improve and generalize some known oscillation criteria due to A.Wintner, I.V.Kamenev for the undamped linear differential equations, and Sobol, J.S.W.Wong for the damped linear differential equations.     

中立型二阶非线性微分方程振动性的判据

Abstract. In this paper ,the oscillation criteria for the solutions of the nonlinear differential e-quations of neutral type of the forms:     

OSCILLATING CRITERIA FOR CERTAIN EVEN ORDER NEUTRAL DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

By using the integral averaging technique, oscillating criteria for certain even order neutral differential equation with deviating arguments are established. These results extend some known oscillation criteria due to Xu and Xia.     

OSCILLATION CRITERIA FOR STRONGLY SUPERLINEAR AND STRONGLY SUBLINEAR HIGHER ORDER DYNAMIC EQUATIONS ON TIME SCALES

We establish some new criteria for the oscillation of even order nonlinear dynamic equation. We study the case of strongly super-linear and the case of strongly sub-linear subject to various conditions.     

OSCILLATION CRITERIA FOR SECOND-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH CONTINUOUS VARIABLE

Some new oscillation criteria are given for a second order nonlinear difference equation with continuous variable. Our results generalize and improve the recent criteria of Zhang Z.G., Bi P. and Chen J.F..     

具有连续分布偏差变元的双曲型微分方程振动准则的进一步结果(英文)

A class of hyperbolic equations with continuous distributed deviating arguments is considered and its oscillation theorems are discussed.These theorems are of higher degree of generality and deal with the cases which are not covered by the known criteria.Particularly,these criteria extend and unify a number of existing results.     

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 SECOND ORDER NEUTRAL DIFFERENCE EQUATION WITH CONTINUOUS VARIABLE

In this paper, we are concerned with the second order neutral difference equation with continuous variable. Using the integral transformation and generalized Riccati transformation, we obtain some oscillation criteria.     

OSCILLATION THEOREMS FOR SECOND ORDER QUASILINEAR PERTURBED DIFFERENTIAL EQUATIONS

Abstract. New oscillation criteria for the second order perturbed differential equation are pre-sented. The special case of the results includes the corresponding results in previous papers,extends and unifies a number of known results.     

一类高阶两项微分方程的振荡原则

研究一类高阶两项微分方程的振荡原则,利用变分原理及微分方程振荡性的扰动理论得到了此类微分方程的振荡与非振荡原则.     

Note on Wong's paper

Using the method of interval integral average, we establish some new oscillation criteria which improve the oscillation criteria due to James S.W. Wong.     

二阶非线性阻尼方程的振动准则

利用Riccati变换和积分平均方法,研究了一类具有阻尼项的二阶非线性方程的解为振动的若干充分条件,建立了一些判定上述方程为振动的充分准则,结果推广并加强了已有的一些振动准则·     

Recent development in oscillatory properties of certain differential equations

In this paper, we summarize some recent oscillation criteria for second order nonlinear differential equations and systems of differential equations, some known oscillation criteria for second order linear differential equations are also involved, and we point out the origin of theses criteria.     

Oscillation criteria of a class of fourth order differential equations

In the present paper, we consider the oscillation of a class of self‐adjoint fourth order differential equation. Some oscillation and non‐oscillation criteria on a perturbation equation of Euler differential equation are given. In particular, we find the exact value of a constant in some oscillation criteria, which has answered the open problem presented by Do?lý in 2004. Copyright © 2011 John Wiley & Sons, Ltd.     

OSCILLATION CRITERIA FOR SECOND ORDER DIFFERENCE EQUATIONS OF NEUTRAL TYPE WITH MIXED ARGUMENTS

In this paper, we establish some new oscillation criteria for second order difference equations of neutral type with mixed arguments. We extend some known oscillation criteria for second order difference equations.     

OSCILLATION CRITERIA FOR CERTAIN NONLINEAR DIFFERENCE EQUATIONS

1 IntroductionIn a number of recent papers [l-61 oscil1ation of solutions of second ordernonlinear difference equations has been investigated. ln this paper, we studythe oscil1atory behavior of solutions of the second order nonlinear differenceequationA(r.--lAx.--l) p.f(x.) = 0, n = l, 2,'' (1)where the difference operator a is defined by Ax. = xn 1 -- xn) n = 1, 2,' ')and the functions r, p, f are to be specified in the following text. By a solutionof Eq.(1), we mean a real sequence x = …     

带次线性中立项的二阶广义Emden-Fowler微分方程的Philos型振动准则

研究一类带次线性中立项的二阶非线性广义Emden-Fowler时滞微分方程的振动性.利用Riccati变换和不等式技巧,在非正则条件下建立了该类方程多个简便的Philos型和Kamenev型新振动准则.所得定理也适应于包括经典Euler方程等线性非中立型方程,推广和改进了已有文献中的相应结果.最后还给出应用实例展示了所得定理是有效和便捷的.     

二阶非线性带有阻尼项微分方程的一个振荡定理

在这篇文章中,利用Riccati变换和积分不等式,对非线性带有阻尼项微分方程,我们给出了—个新的振荡解的判别准则.特别是我们给出的判别准则是比较宽的.     

脉冲中立型时滞抛物方程的振动性

本文研究了一类脉冲中立型时滞抛物方程解的振动性及强振动性,获得了此类脉冲中立型时滞抛物方程解振动和强振动的代数判据.