On behavior of two third-order nonlinear difference equations - Gan, Chenquan,; Yang, Xiaofan,; Liu, Wanping, (Utilitas Mathematica, 2014)
This paper is intended to investigate the oscillation and global stability of positive solutions of the nonlinear difference equation = (Yn-1Y pn-2 + 1)/(yn-1 +ypn-2),n = 0,1,2,•••, where the initial conditions y-2,Y-1,Y0 E (0, +∞), and the parameter p ε [0,1]. By employing the oscillation character, it is found that the unique positive equilibrium is globally asymptotically stable. Additionally, some analogous results are also established for the corresponding difference equation yn+1 = (yn-1 + ypn-2)/(yn-1ypn-2 + 1).