Asymptotic Convergence of the Solutions of a Discrete Equation with Two Delays in the Critical Case

A discrete equation with two integer delays and is considered for . We assume , where and . Criteria for the existence of strictly monotone and asymptotically convergent solutions for are presented in terms of inequalities for the function . Results are sharp in the sense that the criteria are valid even for some functions with a behavior near the so-called critical value, defined by the constant . Among others, it is proved that, for the asymptotic convergence of all solutions, the existence of a strictly monotone and asymptotically convergent solution is sufficient.

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