A second-order nonlinear difference equation: Oscillation and asymptotic behavior

Discrete analogues are investigated for well-known results on oscillation, growth, and asymptotic behavior of solutions of y″ + q(t) y^γ = 0, for q(t) ? 0 and for q(t) ? 0. The analogue of Atkinson's oscillation criterion is shown to be true for Δ²y_{n ? 1} + q_ny_n^γ = 0, but the analogue for Atkinson's nonoscillation criterion is shown to be false.