Asymptotic behavior of solutions for neutral difference equations

The boundedness and asymptotic behavior of all solutions of the neutral delay difference equation Δ(xn − pnxn−k) + qnxn−l = 0, n = 0,1,2,…, are investigated, where Δ is the forward difference operator, k,l are positive integers, {Pn} is a sequence of real numbers and {qn} is a sequence of nonnegative real numbers. The obtained sufficient conditions improve the existing results in the literature.