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We construct the asymptotics for solutions of the higher-order scalar difference equation that is equivalent to the linear delay difference equation ∆y(n) = −g(n)y(n − k) . We assume that… Click to show full abstract
We construct the asymptotics for solutions of the higher-order scalar difference equation that is equivalent to the linear delay difference equation ∆y(n) = −g(n)y(n − k) . We assume that the coefficient of this equation oscillates at the certain level and the oscillation amplitude decreases as n → ∞ . Both the ideas of the centre manifold theory and the averaging method are used to construct the asymptotic formulae. The obtained results are applied to the oscillation and stability problems for the solutions of the considered equation.
Journal Title: Turkish Journal of Mathematics
Year Published: 2020
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