Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation

In this paper, necessary and sufficient conditions for the oscillation and asymptotic behaviour of solutions of the second order neutral delay differential equation (NDDE)

二阶中立型微分方程的振动准则

研究了一类具有连续偏差变元的二阶非线性中立型方程,得到了该类方程的振动准则     

带有振动系数的一类高阶中立型非线性受迫微分方程的振动准则

在本文中,我们获得形如[y(t) l∑j=1pj(t)y(σj(t))](n) ∫0q(t,s)f(y(t s))dσ(s)=h(t)的带有振动系数的一类高阶中立型非线性受迫微分方程的振动准则.     

一类二阶非线性中立型方程的振动准则

获得了一类具连续分布滞量的非线性二阶中立型泛函微分方程所有解振动的若干充分条件.     

Oscillation of nonlinear second order matrix differential equations

In this paper, sufficient conditions are obtained for oscillation of all nontrivial, prepared, symmetric solutions of a class of nonlinear second order matrix differential equations of the form

New oscillation criteria for second order linear matrix differential equations with damping

By using the positive linear functional and the monotone subhomogeneous functional, including the general means and Riccati technique, some new oscillation criteria are established for the second order linear matrix differential system
（P（t）X＇（t））＇ ＋ R（t）X＇（t） ＋ Q（t）X（t） =0, t ≥ to 〉 0
where P（t）, R（t）, Q（t） are n × n real continuous matrix functions, P（t） and R（t） are commutative. Theresults improve and generalize those given in some previous papers, which can be seen by the examples given at the end of this paper.     

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 nonlinear neutral differential equations

By refining the standard integral averaging technique, we obtain new oscillation criteria for a class of second order nonlinear neutral differential equations of the form

(r(t)(x(t)+p(t)x(t-τ))^′)^′+q(t)f(x(t),x(σ(t)))=0.     

Sharp oscillation criteria for second-order neutral delay differential equations

This paper is a continuation of a recent work by the authors on the oscillatory properties of second-order half-linear neutral delay differential equations. Providing a new apriori bound for a nonoscillatory solution, we present a new oscillation criterion, which essentially improves the existing ones. In a particular nonneutral case, the obtained oscillation constant is unimprovable.     

一类二阶中立型偏泛函微分方程组解的振动性

获得了一类二阶中立型偏泛函微分方程组解振动的若干充分条件．     

Oscillation of second order neutral delay differential equations of Emden-Fowler type

We present new oscillation criteria for the second order nonlinear neutral delay differential equation [y(t)-py(t-τ)]'+ q(t)y ^λ (g(t)) sgn y(g(t)) = 0, t ≧ t ₀. Our results solve an open problem posed by James S.W . Wong [24]. The relevance of our results becomes clear due to a carefully selected example. This revised version was published online in June 2006 with corrections to the Cover Date.     

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:     

Generic oscillations of second order delay differential equations with impulses

In this paper, we will study generic oscillation and generic nonoscillation of second order impulsive delay differential equations. Some necessary and sufficient conditions and sufficient conditions are obtained for both phenomena based on the root of characteristic equation.     

Periodic solutions for a kind of second order neutral functional differential equations

In this paper, criteria are established for the existence of periodic solutions to a second order sublinear neutral differential equation. Our method is based on careful a priori estimation and continuation theorem, and our sublinear condition is an improvement of the boundedness condition in some recent results.     

Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities

We present new oscillation criteria for the second order forced ordinary differential equation with mixed nonlinearities:

     

Integral averages and oscillation of second order sublinear differential equations

New oscillation criteria are given for the second order sublinear differential equation

Oscillation criteria for differential equations of second order

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form

Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential

In the case of oscillatory potentials, we give sufficient conditions for the oscillation of the forced super-linear equation

This answers a question raised by J. S. W. Wong.

     

Linearized oscillations for higher order neutral differential equations

In this paper, the oscillation of certain nonlinear neutral differential equations has been studied with the help of the oscillation of associated linear neutral differential equations