连续变量一阶中立型差分方程的振动性

Oscillation of First Order Neutral Difference Equations with Continuous Arguments

研究了具有连续变量的一阶中立型差分方程的振动性 .在中立项系数 p>1和 0≤ p<1这 2种情形下 ,利用积分变换 ,将此类差分方程变换为相应的微分方程或微分不等式 ,得出了新变量的一些重要性质 ;然后用反证法和构造序列的方法 ,同时运用微分方程理论中的一些重要成果 ,得出了差分方程解振动的若干充分条件 ,并给出具体实例加以说明 .

The oscillation of first order neutral difference equations with continuous arguments is investigated when the neutral coefficient 0≤p<1 and p>1.First,several lemmas are given by using the integral transformations,so that the difference equations are converted into the corresponding differential equations and inequalities,and some important properties of new variable are obtained.Then,with the help of some good results of differential equations theory,some sufficient conditions for all solutions of the equations to be oscillatory are obtained,moreover,some examples are given.The way is to proof by contradiction and construct sequence.