Classification and existence of nonoscillatory solutions of higher order nonlinear neutral difference equations

In this paper, we consider the higher order nonlinear neutral delay difference equation of the form Δr(xn + px n-τ) + f(n, xn-σ-1 (n), x n-σ2(n),... , xn-σm(n)) = 0. We give an integrated classification of nonoscillatory solutions of the above equation according to their asymptotic behaviours. Necessary and sufficient conditions for the existence of nonoscillatory solutions with designated asymptotic properties are also established. © 2005 Korean Society for Computational & Applied Mathematics and Korean SIGCAM.