本文了研究m阶混合型中立泛函差分方程:△m（xn+cxn-h+c＊xn+h＊）=k（qxn-g+Pxn+g＊）,k=±1.这里C,C＊,p,q是实数,且h,h＊,g和g＊是正整数,并且对于上述方程建立了一些新的振动性准则.本文结果改进了文[1]中的所有定理,并回答了由 Grace S.R.提出的一个公开问题.

Abstract In this article, we study the mth order neutral functional difference equations of mixed type: Am (xn + cxn-h + c*xn+h*) = k(qxn∧g + pxn+g*), k =±1. Where c,c*,p,q are real numbers and h,h*,g and g* are positive integer, and establish some new criteria for the oscillation of such equations. Our results in this paper improve on all theorems in [1], and answer an open problem offered by Grace S. R. in [1].