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.
@article{107681, author = {Jerzy Popenda and Ewa Schmeidel}, title = {On the asymptotically periodic solution of some linear difference equations}, journal = {Archivum Mathematicum}, volume = {035}, year = {1999}, pages = {13-19}, zbl = {1051.39010}, mrnumber = {1684519}, language = {en}, url = {http://dml.mathdoc.fr/item/107681} }
Popenda, Jerzy; Schmeidel, Ewa. On the asymptotically periodic solution of some linear difference equations. Archivum Mathematicum, Tome 035 (1999) pp. 13-19. http://gdmltest.u-ga.fr/item/107681/
Periodic Solutions of First Order Linear Difference Equations, Math. Comput. Modelling 22, 1, 1995, 11-19. (1995) | MR 1343651 | Zbl 0871.39002
The Periodic Solutions of the Second Order Nonlinear Difference Equation, Publ. Mat. 32, 1988, 49-56. (1988) | MR 0939768 | Zbl 0649.39005
On the Asymptotic Behavior of Solutions of Linear Difference Equations, Publ. Mat. 38, 1994, 3-9. (1994) | MR 1291948 | Zbl 0842.39003
On the Asymptotic Behaviour of Solution of Some Difference Equations of Infinite Order, (submitted).