×

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

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.

MSC:

39A20 Multiplicative and other generalized difference equations
39A22 Growth, boundedness, comparison of solutions to difference equations
39A23 Periodic solutions of difference equations
PDFBibTeX XMLCite
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.