Oscillation of second order nonlinear neutral delay difference equations

Abstract

In this paper, we obtain sufficient conditions for the oscillation of all solutions of the second order nonlinear delay difference equation Δ[a n( Δ(x n+p nx g(n))) α]+f(n,x σ(n))=0, where Δ x n = x n+1 − x n is the forward difference operator, { p n } is a sequence of nonnegative real numbers and α⩾1 is a quotient of positive odd integers. Our results extend and improve the known results in the literature. An example that dwell up the advantage of our results is included.