Existence of non-oscillatory solutions of second-order neutral delay difference equations

In this paper, we consider the second-order neutral delay difference equation with positive and negative coefficients Delta (r(n) Delta(x(n) + cs(n-k))) + p(n+1)x(n+1-m) - q(n+1)x(n+1-l) = 0 where c is an element of R, k greater than or equal to 1 and m,l greater than or equal to 0 are integers, {r(n)}(n=n0)(infinity), {p(n)}(n=n0)(infinity) and {qn}(n=n0)(infinity) are sequences of non-negative real numbers. We obtain global results (with respect to c) which are some sufficient conditions for the existences of non-oscillatory solutions.