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On a class of third-order nonlinear difference equations. (English) Zbl 1178.39011
The topic of the paper is the third order rational difference (or iteration) equation $x_{n+1} = A + \frac{x_n^p}{x_{n-1}^q x_{n-2}^r}, \quad n \in \mathbb{N}_0.$ The authors present five theorems containing some conditions on the positive parameters $$p,q,r$$ and $$A$$ that assure either unboundedness of at least one solution or boundedness of all solutions.

MSC:
 39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type 39A22 Growth, boundedness, comparison of solutions to difference equations
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References:
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