# Article

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Keywords:
difference equation; asymptotic behaviour
Summary:
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.
References:
[1] Agarwal R. P., Popenda J.: Periodic Solutions of First Order Linear Difference Equations. Math. Comput. Modelling 22, 1, 1995, 11-19. MR 1343651 | Zbl 0871.39002
[2] Musielak R., Popenda J.: The Periodic Solutions of the Second Order Nonlinear Difference Equation. Publ. Mat. 32, 1988, 49-56. MR 0939768 | Zbl 0649.39005
[3] Popenda J., Schmeidel E.: On the Asymptotic Behavior of Solutions of Linear Difference Equations. Publ. Mat. 38, 1994, 3-9. MR 1291948 | Zbl 0842.39003
[4] Popenda J., Schmeidel E.: On the Asymptotic Behaviour of Solution of Some Difference Equations of Infinite Order. (submitted).

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