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On the asymptotic behavior and periodic nature of a difference equation with maximum. (English) Zbl 1189.39020

Summary: We investigate the asymptotic behavior and periodic nature of positive solutions of the difference equation

x n =maxA x n-1 ,1 x n-2 α ,n0,

where A0 and 0α1. We prove that every positive solution of this difference equation approaches x ¯=1 or is eventually periodic with a period 2,3 or 4.

MSC:
39A23Periodic solutions (difference equations)
39A22Growth, boundedness, comparison of solutions (difference equations)
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