OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF FIRST ORDER FUNCTIONAL DIFFERENTIAL EQUATION WITH PIECEWISE CONSTANT DELAY

ＯＳＣＩＬＬＡＴＯＲＹＡＮＤＡＳＹＭＰＴＯＴＩＣＢＥＨＡＶＩＯＲＯＦＦＩＲＳＴＯＲＤＥＲＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＩＴＨＰＩＥＣＥＷＩＳＥＣＯＮＳＴＡＮＴＤＥＬＡＹＦｅｎｇＹｕｅｃａｉ(冯月才）（ＳｏｕｔｈＣｈｉｎ?..     

OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF FIRST ORDER DIFFERENTIAL EQUATIONWITH PIECEWISE CONSTANTDEVIATING ARGUMENTS

1IntroductionTheexistence,uniqueness,oscillatoryandasymptoticbehaviorofsolutionsofthefirstorderdifferentialequationswithpiecewiseconstantdelayhavebeenstudiedin[1-4].Butoscillatoryandasymptoticbehavioroffirstorderneutraldifferentialequationwithpiecewiseconstantdelayseemtoberarelyconsidered[5,6].Inthispaper,weconsidertheoscillatoryandasymptoticbehavioroffirstordernonlinearneutraldifferentialequationwithpiecewiseconstantdeviatingargumentsoftheformwherecisaconstant,p(t)EC[0, co),fEC(R,R)andxf(x)…     

一阶非线性中立型泛函微分方程的振动性

近年来,关于一阶线性中立型泛函微分方程的振动性已有不少结果,但对于一阶非线性中立型泛函微分方程的振动性结果迄今很少见到。对下列的中立型泛函微分方程其中:P,τ,σ为正常数,Q(t),h(t)∈C[t_0,+∞),Q(t)>0,f(x)∈C(R,R),当x≠0时,Xf(x)>0。本文建立了振动性的两个结果。     

OSCILLATORY BEHAVIOR OF HIGHER ORDER NONLINEAR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION

ＯＳＣＩＬＬＡＴＯＲＹＢＥＨＡＶＩＯＲＯＦＨＩＧＨＥＲＯＲＤＥＲＮＯＮＬＩＮＥＡＲＮＥＵＴＲＡＬＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＦｅｎｇＹｕｅｃａｉ（冯月才）（ＳｏｕｔｈＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔ...     

OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF A CLASS OF FIRST ORDER NEUTRAL DIFFERENTIAL EQUATION WITH PIECEWISE CONSTANT DELAY

The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation.