Huang, Ying Sue; Knopf, Peter M. Boundedness and some convergence properties of the difference equation \(x_{n+1}=\frac{\gamma x_{n-1} + \delta x_{n-2}}{B x_n + D x_{n-2}}\). (English) Zbl 1237.39006 J. Difference Equ. Appl. 18, No. 1, 27-55 (2012). For the difference equation in the title with positive entries it is shown that all solutions are bounded so far as \(\gamma\leq\delta\). In particular, for \(\gamma=\delta\) some solutions converge to 2-periodic solutions. Reviewer: Lothar Berg (Rostock) Cited in 3 Documents MSC: 39A20 Multiplicative and other generalized difference equations 39A22 Growth, boundedness, comparison of solutions to difference equations 39A23 Periodic solutions of difference equations Keywords:rational difference equation; boundedness; periodic solutions; convergence PDFBibTeX XMLCite \textit{Y. S. Huang} and \textit{P. M. Knopf}, J. Difference Equ. Appl. 18, No. 1, 27--55 (2012; Zbl 1237.39006) Full Text: DOI References: [1] Camouzis E., Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures (2008) · Zbl 1129.39002 [2] DOI: 10.1080/10236190701264826 · Zbl 1124.39008 · doi:10.1080/10236190701264826 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.