Asymptotic behavior of solutions of second-order nonlinear delay differential equations with impulses

This paper is concerned with second-order nonlinear delay differential equations with impulses of the form

     

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.     

Asymptotic behavior and stability of second order neutral delay differential equations

We study the asymptotic behavior of a class of second order neutral delay differential equations by both a spectral projection method and an ordinary differential equation method approach. We discuss the relation of these two methods and illustrate some features using examples. Furthermore, a fixed point method is introduced as a third approach to study the asymptotic behavior. We conclude the paper with an application to a mechanical model of turning processes.     

Oscillation of first order delay differential equations with distributed delay

In this paper, we obtain some oscillation criteria for the first order delay differential equation with distributed delay

     

Boundary value problems for first order impulsive delay differential equations with a parameter

In this paper, by means of the method of upper and lower solutions and monotone iterative technique, the existence of maximal and minimal solutions of the boundary value problems for first order impulsive delay differential equations is established.     

Oscillation criteria for nth‐order nonlinear delay differential equations with a middle term

In this article, we establish some new criteria for the oscillation of nth‐order nonlinear delay differential equations of the form provided that the second‐order equation is either nonoscillatory or oscillatory. Examples are given to illustrate the results. Copyright © 2015 John Wiley & Sons, Ltd.     

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     

Linearized oscillation of odd order nonlinear neutral delay differential equations (I)

In this paper, we proved that the odd order nonlinear neutral delay differential equation

[x(t)−p(t)g(x(t−τ))^](n)+q(t)h(x(t−σ))=0     

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.     

The behavior of solutions of second order delay differential equations

In this paper, we study the behavior of solutions of second order delay differential equation

y^″(t)=p₁y^′(t)+p₂y^′(t−τ)+q₁y(t)+q₂y(t−τ),     

一类偶数阶含阻尼项时滞微分方程解的振动性的判定

利用Riccati变换和辅助函数法,对一类偶数阶含阻尼项非线性时滞微分方程建立了判定其所有解振动的若干充分准则.     

Integral averages and oscillation of second order sublinear differential equations

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

On second order differential equations with state-dependent delay

We study existence and uniqueness of solutions for a general class of second order abstract differential equations with state-dependent delay. Some examples related to partial differential equations with state dependent delay are presented.     

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.     

Uniform stability theorems for delay differential equations with impulses

In the paper, we obtain sufficient conditions for the uniform stability of the zero solution of the delay differential equation with impulses

     

Exponential stability for impulsive delay differential equations by Razumikhin method

In this paper, we study exponential stability for impulsive delay differential equation of the form

     

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.     

Non-oscillatory criteria for a class of second order non-linear forced neutral-delay differential equations

In this paper, sufficient conditions are obtained, so that the second order neutral delay differential equation

Stability caused by impulses for delay differential equations

In the present paper sufficient conditions are obtained for the stability of the zero solution of a nonlinear delay differential equation caused by impulses. This work is partially supported by NNSF of China and EYTF of National Educational Committee