一类差分方程的频率振动解

本文讨论了一类差分方程的解的频率振动性,建立了新的频率振动性定理,给出了如下中立型差分方程的解的频率振动的充分条件,从而简化和改进了文献3]中的相应条件与结论：△（xn＋cnxn-k）=f（n,xn-1）,n=0,1,2,…其中k≥1与l≥1均为正整数,1Cn∩∞n=0是一实数列,f是定义在Z×R上的函数。

Frequently Oscillatory Solutions of a class of Difference Equation

In this paper, we discuss the frequently oscillatory behavior of the solutions of a class of difference equation, then we establish a new frequently oscillatory theorem and present the suffcient conditions of the solutions of the following neutral difference equation to be frequently oscillatory,thus we simplify and improve the correspondence conditions and conclusions in △（xn＋cnxn-k）=f（n,xn-1）,n=0,1,2,…where k≥1,I≥1 are all integers, and 1Cn∩∞n=0 is a real sequence, alsofis a function defined on ZxR.