The paper studies the asymptotic behaviour of solutions to a second-order non-linear discrete equation of Emden–Fowler type
$ \Delta^2 u(k) \pm k^\alpha u^m(k) = 0 $
where $ u\colon \{k_0, k_0+1, \dots\}\to \mathbb{R} $ is an unknown solution, $ \Delta^2 u(k) $ is its second-order forward difference, $ k_0 $ is a fixed integer and $ \alpha $, $ m $ are real numbers, $ m\not = 0, 1 $.
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