Oscillation and nonoscillation criteria for second order difference equations with generalized difference operators.

In this study we investigate some new oscillation and nonoscillation criteria and generalize and improve some results in the literatures for second order nonlinear difference equation with generalized difference operators of the form Δ_l,a(p_nΔl;axn) + q_n(Δ_l,ax_n)^β = F (n, x_n, Δ_l,bx_n), where Δ_l,σ is generalized difference operator such that defined as Δ_l,σx_n = x_n+l - σx_n, and F: N × R² → included. [ABSTRACT FROM AUTHOR]