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Monotone solutions of a higher-order neutral differential equation

Zhang G., Migda M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2004

Vol. 44, nr 1

147--162

A continuous function x(t) is said to be (*)-monotone with a positive number τ if x(t) > 0 and (-1)n(x(t) - x(t - τ))(n) ≥ 0 for n ≥ 0. This paper is concerned with various classifications of (*)-monotone solutions of a neutral differential eąuation. Necessary and/or sufficient conditions are then derived for the existence of these solutions.