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Articles

Asymptotic formulae for solutions of linear second-order difference equations

Pages 107-139 | Received 05 Jan 2015, Accepted 23 Jul 2015, Published online: 07 Mar 2016
 

Abstract

We study asymptotic behaviour of solutions to the (nonoscillatory) linear difference equation Δ(rkΔyk)=pkyk+1, where p,r are positive sequences defined on {m,m+1,m+2,}Z. We establish sufficient conditions (in terms of regular variation) for all eventually positive solutions to satisfy certain asymptotic formulae. As a by-product, we obtain regular variation of all these solutions and some other of their properties. Various related problems are discussed and several examples are given.

AMS Subject Classification:

Acknowledgements

The author thanks the both anonymous referees for their careful reading of the manuscript and helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by RVO 67985840.

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