具连续变量脉冲时滞差分方程的振动性

Oscillation for Impulsive Delay Difference Equations with Continuous Arguments

利用构造辅助方程的方法,建立了无脉冲的具连续变量时滞差分方程与有脉冲具连续变量时滞差分方程在振动性上的等价性,然后利用反证法、构造序列法和积分中值定理等方法,研究了无脉冲的具连续变量时滞差分方程的振动性,得到了方程所有解振动的两个充分性条件,从而得到了具有连续变量脉冲时滞差分方程的所有解振动的两个充分性条件。

First,constituted the equipollence between difference equations without impulses and difference equations with impulses on oscillation,by means of constructing assistant equations.Then,using reduction to absurdity,constructive sequence method and mean value theorem of integrals,studied oscillation for difference equations without impulses,two sufficient conditions on oscillation of all solutions are obtained.Accordingly,two sufficient conditions on oscillation for impulsive delay difference equations with continuous arguments are obtained.