A CLASS OF SECOND ORDER NEUTRAL DIFFERENTIAL INEQUALITIES WITH DISTRIBUTED TYPE DEVIATING ARGUMENTS

ＡＣＬＡＳＳＯＦＳＥＣＯＮＤＯＲＤＥＲＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＩＮＥＱＵＡＬＩＴＩＥＳＷＩＴＨＤＩＳＴＲＩＢＵＴＥＤＴＹＰＥＤＥＶＩＡＴＩＮＧＡＲＧＵＭＥＮＴＳ（傅希林）￥ＦｕＸｉｌｉｎ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＳｈａｎｄｏｎｇＮｏｒ...     

一类具有无穷时滞中立型非稠定脉冲随机泛函微分方程积分解的存在性

本文讨论了一类具有无穷时滞中立型非稠定脉冲随机泛函微分方程,利用Sadovskii不动点原理等工具得到了其积分解的存在性,给出其在一类二阶无穷时滞中立型非稠定脉冲随机偏微分方程积分解的存在性中的应用.     

脉冲中立型时滞微分方程的振动性

证明了线性脉冲中立型时滞微分方程解的振动性等价于一类非脉冲中立型时滞微分方程解的振动性,应用这一结果建立了此类线性脉冲中立型微分方程解的振动性的显示判据。     

脉冲中立型时滞微分方程的正解的存在性

本文证明了线性脉冲中立型微分方程 [y(t)+p(t)y(t-τ)-r(t)y(t-ρ)]′+q(t)y(t-σ)=0,t≥0,t≠t_k, y(t_k~+)-y(t_k)=b_ky(t_k),k=1,2,…正解的存在性等价于一类非脉冲中立型方程正解的存在性,应用这一结果,建立了此类线性脉冲中立型微分方程正解存在性的若干充分条件。     

Asymptotic properties of solutions to linear non-autonomous neutral differential equations

In this article we study asymptotic properties of solutions to first order linear neutral differential equations with variable coefficients and constant delays. Results are stated in terms of the solution to a characteristic equation. By doing this, we extend some of the results obtained for delay equations in [J.G. Dix, Ch.G. Philos, I.K. Purnaras, An asymptotic property of solutions to linear non-autonomous delay differential equations, Electron. J. Differential Equations 2005 (2005) 1-9] to neutral equations.     

On a new class of abstract neutral differential equations

In this work we introduce a new class of abstract neutral differential equations and study the existence of mild and strict solutions. Some concrete applications involving partial neutral differential equations are considered.     

高阶中立型泛函微分方程的周期解

运用迭合度理论和分析的技巧,研究一类具分布时滞的中立型高阶泛函微分方程,并得到了其周期解存在的充分条件。     

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。     

高阶脉冲中立型偏泛函微分方程的强迫振动性

研究一类具高阶Laplace算子的高阶脉冲非线性中立型偏泛函微分方程的强迫振动性,利用Green公式和微分不等式方法将所讨论的脉冲中立型偏微分方程转化为脉冲中立型微分不等式的问题,获得了这类方程在三类不同边值条件下所有解强迫振动的若干充分条件.     

OSCILLATION OF NEUTRAL HYPERBOLIC DIFFERNTIAL EQUATION

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｕｒｐｏｓｅｏｆｔｈｉｓｐａｐｅｒｉｓｔｏｅｘｔｅｎｄｓｏｍｅｏｓｃｉｌａｔｉｏｎｒｅｓｕｌｔｓｏｆｔｈｅｐａｐｅｒｓ［１，２］ｔｏｔｈｅｎｅｕｔｒａｌｈｙｐｅｒｂｏｌｉｃｄｉｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｏｆｔ...     

具非线性中立项的二阶时滞微分方程的振动性质

By using the averaging technique, we obtain new oscillation criteria for second order delay differential equation with nonlinear neutral term. These results generalize and improve some known results about neutral delay differential equation of second order.     

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.     

带强迫项高阶中立型微分方程的振动性和非振动性

我们给出一类强迫高阶非线性中立型时滞微分方程一切解振动的充分条件.而且,也研究了一类强迫一阶中立型方程非振动解的渐近性.     

An Estimate for Distance Between Adjacent Zeroes of Solutions of Neutral Equations

ＡｎＥｓｔｉｍａｔｅｆｏｒＤｉｓｔａｎｃｅＢｅｔｗｅｅｎＡｄｊａｃｅｎｔＺｅｒｏｅｓｏｆＳｏｌｕｔｉｏｎｓｏｆＮｅｕｔｒａｌＥｑｕａｔｉｏｎｓＺｈｏｕＹｏｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉａｎｇｔａｎＵｎｉｖｅｒｓｉｔｙ，Ｈｕ...     

Oscillation criteria for first-order neutral differential equations

This paper discusses a class of first-order neutral differential equations with variable coefficients and variable deviations. A series of sufficient conditions are established for all solutions of the equations to be oscillatory, and some of the conditions are sharp.     

Notes on Oscillation of Solution for aCertain Second Order Neutral Equation

Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｃｏｎｓｉｄｅｒｏｓｃｉｌｌａｔｏｒｙｏｆｅｑｕａｔｉｏｎ（１）［ｘ（ｔ）＋ｃｘ（ｔ－τ）］″＋∫ｂａｐ（ｔ，ξ）ｘ［ｇ（ｔ，ξ）］ｄσ（ξ）＝０，（１）ｗｈｅｒｅτ０；ｐ（ｔ，ξ），ｇ（ｔ，ξ）∈Ｃ（［ｔ０，＋∞）×［ａ，ｂ］，Ｒ）；ｇ（ｔ，ξ）ｔ，ξ∈［ａ，ｂ］；ｇ（ｔ，ξ）ａｒｅｎｏｎ－ｄｅｃｒｅａｓｉｎｇｗｉｔｈｔｏｔ，ξ，ｒｅｓｐｅｃｔｉｖｅｌｙａｎｄｌｉｍｔ→＋∞ｍｉｎξ∈［ａ，ｂ］｛ｇ（ｔ，ξ）｝＝＋∞，σ（ξ）∈（［ａ，ｂ］，Ｒ）ｉｓｎｏｎｄｅｃｒ…     

Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching

Recently, numerical solutions of stochastic differential equations have received a great deal of attention. It is surprising that there are not any numerical methods established for neutral stochastic delay differential equations yet. In the paper, the Euler–Maruyama method for neutral stochastic delay differential equations is developed. The key aim is to show that the numerical solutions will converge to the true solutions under the local Lipschitz condition.     

RAZUMIKHIN-TYPE THEOREMS OF NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.     

Stability analysis of block boundary value methods for the neutral differential equation with many delays

This paper mainly deals with the asymptotic stability properties of block boundary value methods (B₂VMs) for the neutral differential equation with many delays. For the time lagging arguments, a technique of Lagrange interpolation is considered. Under some certain conditions, it is proved that B₂VMs can preserve the asymptotic stability of exact solutions for the neutral differential equation with many delays if and only if B₂VMs are A-stable for ordinary differential equation. Moreover, some numerical experiments are given to confirm the main conclusion.     

奇阶中立型微分方程的振动性

我们给出一类奇阶中立型微分方程的一切解均为振动的充分条件.