Existence of nonoscillatory solutions of higher-order neutral difference equations with general coefficients Original Research Article

In this paper, we consider the following higher-order neutral difference equation: Δm (xn + cxn−k) + pnxn−r = 0, n ≥ n0, where c ϵ View the MathML source, m ≥ 1 is an odd integer, k ≥ 1, r ≥ 0 are integers, {pn}n=n0∞ is a sequence of real numbers. We obtain the global result (with respect to c) for general {pn}, which means that we allow oscillatory {itpn}. The main result is a sufficient condition for the existence of nonoscillatory solutions.