On the dynamics of certain higher-order scalar difference equation: asymptotics, oscillation, stability

Authors

PAVEL NESTEROV

DOI

10.3906/mat-1912-89

Abstract

We construct the asymptotics for solutions of the higher-order scalar difference equation that is equivalent to the linear delay difference equation $\Delta y(n)=-g(n)y(n-k)$. We assume that the coefficient of this equation oscillates at the certain level and the oscillation amplitude decreases as $n\to\infty$. 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.

Keywords

Center manifold, method of averaging, asymptotics, discrete delay equation, oscillation

First Page

1612

Last Page

1639

Recommended Citation

NESTEROV, PAVEL (2020) "On the dynamics of certain higher-order scalar difference equation: asymptotics, oscillation, stability," Turkish Journal of Mathematics: Vol. 44: No. 5, Article 7. https://doi.org/10.3906/mat-1912-89
Available at: https://journals.tubitak.gov.tr/math/vol44/iss5/7