具有可变时滞的高阶非线性非自治差分方程的振动性

Oscillation of Higher Order Nonlinear Nonautonomous Difference Equations with Variable Delay

研究具有可变时滞的高阶非自治中立型差分方程Δm(xn-cnxn-k)+h(n,xn-ln)=0,n=0,1,2,…的振动性.利用方程的最终正解和最终负解导致序列{Δi(xn-cnxn-k)}(i=0,1,2,…,m-1)的最终单调和保号性,得到了这类差分方程振动的一系列充分条件.

This paper is concerned with the oscillation of higher order nonlinear nonautonomous delay difference equation △^m（xn-CnXn-k）＋h（n,xn-ln）=0,n=0,1,2,… By means of studying eventually positive solution and eventually negative solution of this equation, and the monotony of the sequences {△′（xn-cnxn-k）}（i=0,1,2,…,m-1）. Some sufficient conditions of oscillation for this equation are obtained.