Geodesic
On the asymptotically periodic solution of some linear difference equations
Archivum mathematicum, Tome 35 (1999) no. 1, pp. 13-19 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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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/

[1] Agarwal R. P., Popenda J.: Periodic Solutions of First Order Linear Difference Equations. Math. Comput. Modelling 22, 1, 1995, 11-19. | MR | Zbl

[2] Musielak R., Popenda J.: The Periodic Solutions of the Second Order Nonlinear Difference Equation. Publ. Mat. 32, 1988, 49-56. | MR | Zbl

[3] Popenda J., Schmeidel E.: On the Asymptotic Behavior of Solutions of Linear Difference Equations. Publ. Mat. 38, 1994, 3-9. | MR | Zbl

[4] Popenda J., Schmeidel E.: On the Asymptotic Behaviour of Solution of Some Difference Equations of Infinite Order. (submitted).