Nonoscillatory solutions of second order nonlinear difference equations

In this paper, we will study the nonoscillatory solution of the second order nonlinear difference equation Δ(|Δxn-1|α-1Δxn-1)+qn|xn|β-1xn=0, where {qn}n=0∞ is a nonnegative sequence and β>α>0. New sufficient conditions are established for the existence of nonoscillatory solutions of the equation, which generalize and complement the main result in [Y.G. Sun, Oscillation and nonoscillation for second-order linear difference equations, Appl. Math. Comput. 170 (2005) 1095-1103].