### A Massera-type criterion for almost periodic solutions of higher-order delay or advance abstract functional differential equations.

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In this paper, using Mawhin's continuation theorem of the coincidence degree theory, we obtain some sufficient conditions for the existence of positive almost periodic solutions for a class of delay discrete models with Allee-effect.

A neutral impulsive system with a small delay of the argument of the derivative and another delay which differs from a constant by a periodic perturbation of a small amplitude is considered. If the corresponding system with constant delay has an isolated ω-periodic solution and the period of the delay is not rationally dependent on ω, then under a nondegeneracy assumption it is proved that in any sufficiently small neighbourhood of this orbit the perturbed system has a unique almost periodic solution....

The paper is the extension of the author's previous papers and solves more complicated problems. Almost periodic solutions of a certain type of almost periodic linear or quasilinear systems of neutral differential equations are dealt with.