一类非线性时滞差分方程解的振动性和非振动性

Oscillation of Solutions of the Delay Difference Equations with a Nonlinear Neutral Term

在α>1且0<β≤α的情形下研究了具非线性中立项时滞差分方程Δ(xn-pxnα-T)+qnxnβ-σ=0,n≥n0正解的存在性,获得了几乎“sharp”振动和非振动准则,及在α=p=1,β∈(0,∞)的情形下上述方程解的振动性,获得了一些新的振动条件.

The oscillatory behavior and non-oscillatory behavior of solutions of the delay difference equations with nonlinear neutral term △（xn-pxαn-T）＋qnxβn-σ=0,n≥n0 are studied in the case when α 〉 1 and 0〈 β≤α. One almost ＂sharp＂ oscillatory and non-oscillatory criteria is obtained, and the ocsillatory behavior of this equation is studied in the case when a = p = 1, β∈ （0, ∞ ）.