OSCILLATION OF FIRST ORDER NONLINEAR IMPULSIVE DIFFERENTIAL EQUATIONS WITH MIXED ARGUMENT

This paper devotes to study the oscillatory behavior of solutions of a first order nonlinear impulsive differential equation with mixed argument. First, without assuming the deviating argument to be retarded or advanced, a sufficient condition is established for all solutions of the differential equation to be oscillatory. Next, a sufficient condition for the differential equation to have nonoscillatoty solution is given. Finally, a sufficient and necessary condition for all solutions of the differential equation to be oscillatory is obtained.     

二阶拟线性中立型时滞微分方程的振动性

考虑二阶中立型时滞微分方程[a(t)|(x(t) p(t)x(t-τ)）′|^α-1(x(t) p(t)x(t-τ））′]′ f(t,x(t-σ））=0(E)其中α，τ，σ是非负常数，a(t),p(t)∈C([t0,∞），R），f(t,x)∈C(R,R)。建立了方程（E）的一些新的振动条件。     

OSCILLATIONS OF SECOND ORDER DIFFERENTIAL EQUATIONS WITH IMPULSES

１ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｐａｐｅｒ，ｗｅｃｏｎｓｉｄｅｒｔｈｅｓｅｃｏｎｄ－ｏｒｄｅｒｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｗｉｔｈｉｍｐｕｌｓｅｓａｓ（ｒ（ｔ）ｘ′）′＋ｆ（ｔ，ｘ）＝０，ｔ≥ｔ０，ｔ≠０，ｋ＝１，２，…，ｘ（ｔ＋ｋ）...     

带强迫项的脉冲时滞微分方程的振动性

研究带一阶强迫项的脉冲时滞微分方程的振动性,借助于Kartsatos变换,得到了若干判别这类方程振动的充分性条件,所得的结果推广并改进了时滞微分方程振动性理论中某些已知的相关结果。     

OSCILLATIONS OF FIRST ORDER NONLINEAR RETARDED DIFFERENTIAL EQUATIONS

ＯＳＣＩＬＬＡＴＩＯＮＳＯＦＦＩＲＳＴＯＲＤＥＲＮＯＮＬＩＮＥＡＲＲＥＴＡＲＤＥＤＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＷａｎｇＱｉｒｕ（王其如）（ＬｕｏｙａｎｇＴｅａｃｈｅｒｓ＇Ｃｏｌｌｅｇｅ，洛阳师范高等专科学校，邮编：４７１０２２）Ａｂｓ...     

高阶混合中立型微分方程解的振动性

本文研究奇数阶混合类型的中立型微分方程[x(t)+cx(t-h)+c*x(t+h*)](n)=qx(t-g)+px(t+g*),这里c,c*,g,g*,h,h*,p和q是实常数,得到关于解振动的一些新的判别准则.本文结果改进了GraceS.R.的全部定理.     

OSCILLATION OF IMPULSIVE HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION WITH DELAY

In this paper, oscillation properties of the solutions of impulsive hyperbolic equation with delay are investigated via the method of differential inequalities. Sufficient conditions for oscillations of the solutions are established.     

超线性时滞微分方程解的振动性

研究一阶超线性时滞微分方程x′(t) p(t)[x(t—γ)]^α＝0(α＞1)解的振动性及非振动性,获得了保证其所有解振动的“almost sharp”准则,并应用所得结果于混合型时滞微分方程x′（t） ∑^ni=1pi（t）[x（t-γi]^αi=0,得到一族振动准则。     

二阶线性时滞微分方程的广义振动性

本文主要研究了二阶线性时滞微分方程的广义振动性和广义非振动性,给出了方程广义振动和广义非振动的一些判定定理,同时给出了一类方程广义非振动的充要条件.     

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.     

CONDITIONS FOR OSCILLATION OF NEUTRAL DELAY DIFFERENTIAL EQUATIONS

In this paper,we study one type of odd-order neutral delay differential equation. Suffcient conditions for the oscillation of every solution to this type of differential equation are given.     

OSCILLATION OF THIRD ORDER DELAY DIFFERENTIAL EQUATIONS WITH IMPULSES

In this paper we study the oscillation and asymptotic behavior of third order delay differential equations with impulses.Some new sufficient conditions which guarantee that every solution is oscillatory or converges to zero are obtained. Three examples are also given to illustrate our main results.     

OSCILLATION THEOREMS FOR DELAY AND NEUTRAL DELAY DIFFERENTIAL EQUATIONS

Oscillation criteria for the delay differential equationx′(t)+p(t)x(t-т(t))=0,where p, т are non-negative real-valued continuous functions are investigated inthe case when the numbers k=integral from n=t-т(t) to t(p(s)ds),L=integral from n=t-т(t) to t(p(s)ds)satisfy 0≤k<1/e and 1/e≤L<1. The present result improves almost allresults of the literature concerning it. Furthermore, it is established that allsolutions of the odd-order neutral delay differential equation(x(t)-px(t-т))~(n)+Q(t)x(t-σ)=0,where 0≤p<1,т,σ∈(0,∞)and Q(t)≥0,are oscillatory ifintegral from n=t-σ to t ((t-s)~(n-1)Q(s)ds>(1/e)(1-p)(n-1))!.This result generalizes a theorem of Gopalsamy et. al (Czech. Math. J., 42(1992),313-323)and also extends a very well-known result of Ladas (ApplicableAnalysls, 9(1979),93-98).     

具有变号系数中立型时滞微分方程的振动性

本文讨论一类一阶具有变号系数中立型时滞微分方程的振动性，建立了此类方程一切解振动的几族充分条件。将其结论用于具有正系数中立型时滞微分方程及具有正负系数中立型时滞微分方程，改进了[1-8]的相应定理。     

二阶非线性中立型微分方程的振动性

利用广义Riccati变换和权函数积分平均技巧,建立了非线性时滞中立型方程:[r(t)(x(t)-p(t)x(t-τ))']'+q(t)f(x(t-δ))h(x'(t))=0的振动准则,其中τ和δ是非负常数,a,p,q∈C([to,∞),R),f和h∈C(R,R).这些结果补充了大量存在性结论和处理以前结果不能解决的问题.特别地,以实例说明本文结果是实质性推广.     

一类脉冲时滞双曲型方程组解的振动性

本文研究含脉冲的时滞双曲型方程组解的振动性,利用二阶脉冲微分不等式的性质,得到了方程组在两类不同边界条件下解振动的一些充分判据.     

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 THEOREMS FOR SECOND ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS

ＯＳＣＩＬＬＡＴＩＯＮＴＨＥＯＲＥＭＳＦＯＲＳＥＣＯＮＤＯＲＤＥＲＮＯＮＬＩＮＥＡＲＤＥＬＡＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＪｉｎＭｉｎｇｚｈｏｎｇ（靳明忠）（ＷｕｈａｎＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ）Ａｂｓｔｒａｃｔ：Ｓｏｍ...     

EXISTENCE RESULTS FOR IMPULSIVE NEUTRAL EVOLUTION DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

This paper is mainly concerned with the existence of mild solutions to a first order impulsive neutral evolution differential equations with state-dependent delay. By suitable fixed point theorems combined with theories of evolution systems,we prove some existence theorems. As an application,an example is also given to illustrate the obtained results.     

时滞微分方程和脉冲时滞微分方程解的存在唯一性

本文研究了时滞微分方程的问题.利用上下解作为耦合初始迭代得到一个收敛于此方程解的单调序列的方法,获得了时滞方程和脉冲时滞微分方程解的存在唯一性结果,推广了文献[3,5]的相关结果.