On the Asymptotically Periodic Solution of Some Linear Difference Equations

Jerzy Popenda and Ewa Schmeidel

Address. Institute of Mathematics, Poznan University of Technology, Piotrowo 3a, 60-965 Poznan, POLANDe

E-mail: jpopenda@math.put.poznan.pl, eschmeid@math.put.poznan.pl

Abstract. 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.

AMSclassification. 39A10.

Keywords. Difference equation, asymptotic behaviour.