Stević, Stevo On the recursive sequence \(x_{n+1}=\frac{\alpha+\beta x_{n-k}}{f(x_n,\dots,x_{n-k+1})}\). (English) Zbl 1100.39014 Taiwanese J. Math. 9, No. 4, 583-593 (2005). The paper discusses qualitative properties for the solutions of the difference equation \[ x_{n+1}= {{(\alpha+\beta x_{n-k})}\over{f(x_n,\ldots,x_{n-k+1})}} \] with \(\alpha\geq 0\;,\;\beta\geq 0\) and \(f:\mathbb R_+^k\to\mathbb R_+\) continuous and non-decreasing in each argument such that \(f(0,0,\ldots,0)>0\). Only nonnegative solutions are considered. Several cases are tackled: \(\beta<1\); \(\beta>1\); \(\beta=1, \alpha>0\). An open problem is finally stated. Reviewer: Vladimir Răsvan (Craiova) Cited in 1 ReviewCited in 21 Documents MSC: 39A11 Stability of difference equations (MSC2000) 39A20 Multiplicative and other generalized difference equations Keywords:rational difference equation; positive solution; oscillation; boundedness; stability PDFBibTeX XMLCite \textit{S. Stević}, Taiwanese J. Math. 9, No. 4, 583--593 (2005; Zbl 1100.39014) Full Text: DOI