OSCILLATION RESULTS FOR A SECOND ORDER NEUTRAL DELAY DIFFERENTIAL EQUATIONS

Some new oscillation criteria are established for a second order neutral delay differential equations. These results improve oscillation results of Y.V. Rogo-vchenko for the retarded delay differential equations. The relevance of our theorems is illustrated with two carefully selected examples.     

OSCILLATION CRITERIA FOR SECOND ORDER QUASILINEAR NEUTRAL EQUATION

We present some new oscillation criteria for second order neutral delay differential equations with distributed deviating argument using the Riccati technique and some inequalities. The results obtained improve and extend some known results.     

A NEW OSCILLATION CRITERION FOR FIRST ORDER NEUTRAL DELAY DIFFERENTIAL EQUATION

In this paper, a new sufficient condition for the oscillation of all solutions of first order neutral delay differential equations is obtained. Secondly, the result can also be extended to a general neutral differential equation, and many known results in the literatures are improved.     

OSCILLATION FOR A CLASS OF SECOND ORDER DELAY DIFFERENTIAL EQUATIONS WITH NONLINEAR NEUTRAL TERM

By the averaging technique,we establish some oscillation theorems for a class of second order delay differential equations with nonlinear neutral term,the results obtained extend 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.     

Oscillation of a Second-order Impulsive Neutral Differential Equation

Oscillation theorems for a second-order impulsive neutral differential equation are established, which extend the main results developed by Li et alLi et al, Oscillation of second order self-coajugate differential equation with impuls[es. J Comput Appl Math 197（2006）： 78-88] to the considered equation. Two examples are also inserted to illustrate our main results.     

On the Existence of Periodic Solutions for a Kind of Second Order Neutral Functional Differential Equation

By means of the continuation theorem of coincidence degree theory, some new results on the non-existence, existence and unique existence of periodic solutions for a kind of second order neutral functional differential equation are obtained.     

OSCILLATION CRITERIA FOR DELAY DIFFERENTIAL EQUATIONS WITH IMPULSES

The present paper is devoted to the investigation of the oscillation of second order nonlinear delay differential equation (DDE) with impulses, sufficient conditions of oscillation for the solutions of DDE with impulses are obtained by using differential inequality. Some known results are improved and generalized.     

OSCILLATIONS OF SOLUTION FOR A CLASS OF HIGHER-ORDER NEUTRAL DIFFERENTIAL EQUATION

In this paper, the higher order neutral differential equation with continuous distributed delay is concerned and the oscillatory criteria are given.     

OSCILLATION CRITERIA FOR SECOND ORDER FUNCTIONAL NEUTRAL DIFFERENTIAL EQUATIONS

By the standard integral averaging technique, we obtain some oscillation criteria for a second order functional neutral differential equation. Our results are more general than those in B. Baculíková, J. Dzurina [2]. An example is provided to illustrate the relevance of our theorems.     

具连续分布滞量的二阶中立型方程的振动性定理

利用直接分析方法研究一类具有连续分布滞量的二阶非线性中立型方程解的性质，获得了类具连续分布滞量的二阶非线性中立型泛函微分方程所有解振动的若干充分条件．     

非线性二阶中立型微分方程的振动性

考虑中立型微分方程我们建立了方程(1)的若干振动准则。这些结果适用于强超线性和强次线性中立型微分方程,且当p(t)≡0时仍然成立。     

Controllability of second‐order impulsive neutral functional differential inclusions in Banach spaces

In this paper, we shall prove the controllability of second‐order impulsive neutral functional differential inclusions with infinite delay in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families and a fixed point theorem for multi‐valued mappings. As an example, we also consider an second‐order impulsive neutral functional differential equation with infinite delay. Copyright © 2009 John Wiley & Sons, Ltd.     

具无穷时滞高阶中立型微分方程的周期解

利用重合度理论研究了一类具有无穷时滞高阶中立型泛函微分方程周期解的存在性,获得了该方程存在周期解的充分条件,推广和改进了二阶方程的相应结果.     

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.     

On stability of the second order neutral differential equation

There exist a well-developed stability theory for neutral differential equations of the first order and only a few results on functional differential equations of the second order. One of the aims of this paper is to fill this gap. Explicit tests for stability of linear neutral delay differential equations of the second order are obtained.     

二阶中立型变时滞差分方程解的振动性

研究了二阶中立型变时滞差分方程Δ2(xn+pxn-l)+qnf(xσ(n))=0解的振动性,获得了该类方程全部非平凡解振动的三个定理.所得结果将二阶中立型差分方程已有的振动性的相应结论推广到了二阶中立型变时滞差分方程.     

On the behavior of the oscillatory solutions of first or second order delay differential equations

Some new results are given concerning the behavior of the oscillatory solutions of first or second order delay differential equations. These results establish that all oscillatory solutions x of a first or second order delay differential equation satisfy x(t)=O(v(t)) as t→∞, where v is a nonoscillatory solution of a corresponding first or second order linear delay differential equation. Some applications of the results obtained are also presented.