On behavior of two third-order nonlinear difference equations

Abstract

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 +y^p_n-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 y_n+1 = (y_n-1 + y^p_n-2)/(y_n-1y^p_n-2 + 1).