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On the recursive sequence x n+1 =α+βx n-1 γ+x n . (English) Zbl 1039.39004

Summary: We investigate the boundedness character, the oscillatory and periodic nature, and the global stability behavior of the nonnegative solutions of the difference equation

x n+1 =α+βx n-1 γ+x n ,n=0,1,

where the parameters α,β, and γ are nonnegative real numbers.


MSC:
39A11Stability of difference equations (MSC2000)
39A20Generalized difference equations