Abstract
We study asymptotic behaviour of solutions to the (nonoscillatory) linear difference equation , where are positive sequences defined on . 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.
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).