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...     

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.     

带强迫项与阻尼项的二阶非线性微分方程的区间振动性

研究了一类二阶非线性微分方程的振动性.利用广义黎卡提变换和积分平均技巧建立了方程(1)的新的振动准则,推广了文献中已有的一些结果.     

Oscillations of solutions of second order quasilinear differential equations with impulses

Some Kamenev-type oscillation criteria are obtained for a second order quasilinear damped differential equation with impulses. These criteria generalize and improve some well-known results for second order differential equations with /and without impulses. In addition, new oscillation criteria are also obtained to generalize and improve known results. Two examples of applications are given to illustrate the theory.     

时间尺度上具阻尼项的二阶半线性时滞动力方程振动性的新结果

本文讨论一类具阻尼项的二阶半线性时滞动力方程解的振动性质, 利用广义Riccati 变换和不等式技巧, 在一定条件下, 建立了4 个新的振动准则, 其结果改进和推广了已知的一些结果.     

时间尺度上具阻尼项的二阶半线性时滞动力方程的振动准则(Ⅱ)

本文讨论一类具阻尼项的二阶半线性时滞动力方程解的振动性质, 利用广义Riccati 变换和不等式技巧. 在一定条件下, 建立了四个新的振动准则, 改进和推广了已知的一些结果.     

Oscillation of the half-linear PDE in general exterior domains—the variational approach

In the paper a variational technique is used to show how to derive new oscillation criteria for the half-linear partial differential equation via the oscillation criteria for the ordinary half-linear differential equation. In contrast to the results usually found in the literature, general types of unbounded domains can be considered.     

Relative oscillation of linear Hamiltonian differential systems

We discuss the concept of relative oscillation for linear Hamiltonian differential systems. We prove a statement which enables to study this oscillation using the criteria of the classical oscillation theory. We also discuss some other aspects of the problem.     

Oscillation of linear Hamiltonian systems

We establish new oscillation criteria for linear Hamiltonian systems using monotone functionals on a suitable matrix space. In doing so we develop new criteria for oscillation involving general monotone functionals instead of the usual largest eigenvalue. Our results are new even in the particular case of self-adjoint second order differential systems.

     

Oscillatory properties of certain nonlinear fractional nabla difference equations

In this paper, we investigate the oscillation of a class of nonlinear fractional nabla difference equations. Some oscillation criteria are established.     

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.     

二阶非线性微分方程的振动准则

本文给出关于二阶非线性常微分方程和时滞微分方程的一些新的振动准则．