中文摘要：

考虑二阶半线性中立型差分方程△[αn｜△（xn＋pnxn-τ）｜^α-1△（xn＋pnxn-τ）]＋∑i=1^k qi（n）｜xn-σi｜^α-σi=0，（1）给出了方程（1）的解的振动性的充分条件，所有结果推广和改进了关于中立和时滞差分方程已有结果。

英文摘要：

Consider the second-order semi-linear neutral difference equation △[αn｜△（xn＋pnxn-τ）｜^α-1△（xn＋pnxn-τ）]＋∑i=1^k qi（n）｜xn-σi｜^α-σi=0,（1）The sufficient conditions are established for oscillation of the solutions of （1）. These results generalize and improve some known results about both neutral and delay difference equation.