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Asymptotic summation of perturbed linear difference systems in critical case

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We propose an asymptotic summation method for certain class of linear difference systems. Both the ideas of the centre manifold theory and the averaging method are used to construct the… Click to show full abstract

We propose an asymptotic summation method for certain class of linear difference systems. Both the ideas of the centre manifold theory and the averaging method are used to construct the asymptotics for solutions. We illustrate the asymptotic summation method by constructing the asymptotics for solutions of certain higher order scalar difference equation with an oscillatory decreasing coefficient.

Keywords: summation perturbed; difference; asymptotic summation; difference systems; linear difference

Journal Title: Journal of Difference Equations and Applications
Year Published: 2019

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