Geodesic
On the asymptotically periodic solution of some linear difference equations
Archivum mathematicum, Tome 35 (1999) no. 1, pp. 13-19.

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For the linear difference equation \[ x_{n+1} -a_n x_n = \sum _{i=0}^r a_n^{(i)}x_{n+i}, \;\;\; n \in N \] sufficient conditions for the existence of an asymptotically periodic solutions are given.
Classification : 39A10, 39A11
Keywords: difference equation; asymptotic behaviour 
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     title = {On the asymptotically periodic solution of some linear difference equations},
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Popenda, Jerzy; Schmeidel, Ewa. On the asymptotically periodic solution of some linear difference equations. Archivum mathematicum, Tome 35 (1999) no. 1, pp. 13-19. http://geodesic.mathdoc.fr/item/ARM_1999__35_1_a1/