具正负系数的二阶不稳定中立型微分方程的振动性

本文研究了一类具正负系数的二阶不稳定中立型微分方程,得到了方程的所有有界解都振动的充分判据。     

变系数变时滞中立型泛函微分方程解的振动性

变系数变时滞中立型泛函微分方程解的振动性邓飞其（华南理工大学自动化系，广州５１０６４１）徐玉民（东北重型机械学院基础部，齐齐哈尔１６１０４２）文献中关于中立型方程振动性的较多结果具有明显的局限性，如要求一些系数具有周期性、满足某些有界性条件（如０≤Ｐ...     

具有变系数的二阶中立型差分方程的有界振动

研究一类具有连续变量的二阶中立型时滞差分方程，给出了该类方程一切有界解振动的几个充分条件.     

二阶中立型微分方程振动比较定理

首先建立了一个Ｐｉｃｏｎｅ型的恒等式及两个Ｓｔｕｒｍ型的比较定理。利用它们定量地给出一类二阶中立型微分方程所有解振动的充分条件，著名的关于二阶常微分方程的Ｓｔｕｒｍ基本定理为本文定理之特例。     

非线性中立抛物型泛函微分方程解的振动判据

讨论一类多滞量中立抛物型泛函微分方程解的振动性质,获得了其一切解振动的充分条件及线性情况下的充要条件;指出了与普通抛物型偏微分方程质的差异。     

高阶中立型方程有界振动的比较定理

本文在较弱的条件下，研究了高阶线性中立型方程解的渐近性问题，并建立了方程有界振动的比较定理．我们的结果，改进并推广了最近在文［１］中给出的相应结果．     

中立抛物型偏微分方程解的强迫振动

本讨论一类多滞量中立抛物型偏微分方程解的振动性物,获得了其一切解振动的充分条件,指出了与普通抛物型偏微分方程质的差异。     

高阶具“积分小”系数中立型微分方程的振动性

本文提出了一种研究高阶中立型方程「ｘ（ｔ）－Ｐ（ｔ）ｘ（Ｔ－τ）」＾（ｎ）＋Ｑ（ｔ）ｘ（ｔ－δ）＝０,ｔ≥ｔ振动性的新技巧,其中不需要通常的积分发散条件∫＾∞Ｑ（ｓ）ｄｓ＝∞。     

EXISTENCE AND ITERATIVE APPROXIMATIONS OF BOUNDED POSITIVE SOLUTIONS TO A NONLINEAR NEUTRAL DIFFERENTIAL EQUATION

In this paper,we consider a nonlinear neutral differential equation.By the Schauder fixed point theorem,some sufficient conditions are obtained to ensure the existence of uncountably many bounded positive solutions.In addition,we give the iterative approximation sequences with errors for these positive solutions and establish some error estimates between the approximate and the positive solutions.     

OSCILLATION AND EXISTENCE OF POSITIVE SOLUTIONS FOR NEUTRAL DIFFERENTIAL EQUATIONS

ＯＳＣＩＬＬＡＴＩＯＮＡＮＤＥＸＩＳＴＥＮＣＥＯＦＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＦＯＲＮＥＵＴＲＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＳｈｅｎＪｉａｎｈｕａ（申建华）（ＨｕｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，湖南师范大学，邮编４１００...     

一类中立型泛函微分方程周期解问题

本文利用Fourier级数理论和Mawhin重合度拓展定理研究一类中立型泛函微分方程的周期解存在性问题.在其对应的特征方程具有零特征根的条件下,得到了周期解存在性的新结果.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION

The boundedness of the every solution and the asymptotic behavior of all solutions of the nonlinear neutral delay differential equation [x(t) - P(t)x(t - t)]' Q1 (t)f(x{t-σ1))-Q2(t)f(x(t -σ2))=0,t≥t0 are investigated, whereτ,σ1,σ2∈(0,∞), P∈C([t0,∞),R), and Q1,Q2∈C([t0,∞),R), f∈C(R,R). The sufficient conditions obtained improve the existing results in the literatures.     

一阶非线性时滞微分方程解的振动性

本文通过使用化多时滞为单时滞的技巧，研究了一类广泛的非线性泛函微分方程解的振动性，所得结果包含和改进了Hunt，Yorke等多人的结果．     

EXISTENCE OF PERIODIC SOLUTIONS TO A KIND OF n-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

By means of the continuation theorem of coincidence degree theory, we study a kind of n-order neutral functional differential equation. Some new results on the existence of periodic solutions are obtained.     

PERIODIC SOLUTIONS TO A HIGH-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

In this paper,using the principle of a priori boundedness,we study the existence and uniqueness of periodic solutions to a high-order neutral functional differential equation.Some new results for the existence and uniqueness of the periodic solution are obtained.     

中立型抛物方程解的强迫振动性

本文讨论中立型抛物方程解的强迫振动，其中Ω是Rn中具有光滑边界Ω的有界区域，     

OSCILLATION OF A SECOND-ORDER HALF-LINEAR NEUTRAL DAMPED DIFFERENTIAL EQUATION WITH TIME-DELAY

In this paper,the oscillation for a class of second-order half-linear neutral damped differential equation with time-delay is studied.By means of Yang-inequality,the generalized Riccati transformation and a certain function,some new sufficient conditions for the oscillation are given for all solutions to the equation.     

OSCILLATION OF A NONLINEAR DELAY DIFFERENTIAL EQUATION WITH NONLINEAR NEUTRAL TERM

This paper is concerned with the following nonlinear delay differential equation with nonlinear neutral term[h(t)(y(t) +φ(t,y(τ(t)))']' + q(t)f(y(g(t))) = 0. An oscillation criterion for the above equation is obtained.