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

Abstract

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 ∆l,a(pn∆l,axn) + qn(∆l,axn) β = F (n, xn, ∆l,bxn), where ∆l,σ is generalized difference operator such that defined as ∆l,σxn = xn+l − σxn, and F : N × R 2→ R˙ . Also, some examples illustrating the results are included.