Stević, Stevo On the recursive sequence \(x_{n+1}= -1/x_n+ A/x_{n-1}\). (English) Zbl 1005.39016 Int. J. Math. Math. Sci. 27, No. 1, 1-6 (2001). The periodic character of solutions of the nonlinear difference equation \(x_{n+1}=-1/x_{n}+A/x_{n-1}\) is studied. It is shown that, if \(A\in (0,1],\) then every nonequilibrium solution to the above equation (which is well defined for all \(n\in \mathbb{N}\)) converges to the periodic solution \[ \dots ,-\sqrt{A+1},\;\sqrt{A+1},\;-\sqrt{A+1},\;\sqrt{A+1},\dots . \] Reviewer: N.C.Apreutesei (Iasi) Cited in 13 Documents MSC: 39A11 Stability of difference equations (MSC2000) 39B05 General theory of functional equations and inequalities Keywords:periodic solution; asymptotic stability; nonequilibrium solution PDFBibTeX XMLCite \textit{S. Stević}, Int. J. Math. Math. Sci. 27, No. 1, 1--6 (2001; Zbl 1005.39016) Full Text: DOI EuDML