Oscillation of second-order perturbed nonlinear difference equations

摘要

Using the Riccati transformation techniques we will establish some new oscillation criteria for the second-order perturbed nonlinear difference equationΔ(an−1(Δxn−1)γ)+F(n,xn)=G(n,xn,Δxn),n⩾1where γ>0 is a quotient of odd positive integers. Some comparison between our theorems and those previously known results are indicated. Examples are interested in the text to illustrate the relevance of our results.