Monotone Solutions of a Higher-Order Neutral Difference Equation

A real sequence x_k is said to be (*)-monotone with respect to a sequence p_k and a positive integer if x_k > 0 and . This paper is concerned with the existence of (*)-monotone solutions of a neutral difference equation. Existence criteria are derived by means of a comparison theorem and by establishing explicit existence criteria for positive and/or bounded solutions of a majorant recurrence relation.