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Boundedness and some convergence properties of the difference equation x n+1 =γx n-1 +δx n-2 Bx n +Dx n-2 . (English) Zbl 1237.39006
For the difference equation in the title with positive entries it is shown that all solutions are bounded so far as γδ. In particular, for γ=δ some solutions converge to 2-periodic solutions.
MSC:
39A20Generalized difference equations
39A22Growth, boundedness, comparison of solutions (difference equations)
39A23Periodic solutions (difference equations)