Abstract
Abstract A real sequence {xk } is said to be (*)-monotone with respect to a sequence {pk } and a positive integer σ if xk > 0 and (–1) n Δ n (xk – pkxk–σ ) ≥ 0 for n ≥ 0. 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.
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