In this paper, some new oscillation criteria are obtained for the first-order delay difference equation xn+1−xn+kk(k+1)k+1xn-k+f(n,xn−l1,…,xn−ls)=0,n=0,1,2,…,, where k,l1,l2,, ls are positive integer numbers, f is a function. Our results improve the known results in the literature. And some examples are given to demonstrate the advantage of our results.

New oscillation criteria for the second order perturbed differential equation are presented. The special case of the results includes the corresponding results in previous papers,extends and unifies a number of known results.