具有可变时滞的二阶中立型差分方程的振动和非振动准则

摘要

中立型时滞泛函差分方程的振动性在理论和应用中有着重要意义.本文研究了一类具有可变时滞的二阶非线性中立型泛函差分方程,首先,利用Banach空间的压缩映照不动点定理,得到了该方程存在有界的最终正解的充分条件;其次,通过引入Riccati变换并结合一些分析技巧,得到了该方程振动的若干充分条件,所得定理推广并改进了现有文献中的一些结果,并同时给出了说明定理应用的例子.%The oscillation of neutral delay functional difference equation has important implications in both theory and application.In this paper,a class of second order nonlinear neutral functional difference equations with variable delays are studied.First,using the fixed point theorem in Banach space,the criteria for existence of the bounded eventually positive solution is obtained.Second,by generalized Riccati transformation and some necessary analytic techniques,some sufficient conditions for oscillation of the equation are given.Some results available in documents are extended in this paper.Illustrative examples are given.