New criteria for the oscillation and existence of monotone solutions of second-order nonlinear difference equations

摘要

We obtain sufficient conditions for the oscillation of the perturbed difference equation Δ(an−1(Δyn−1)σ)+F(n,yn)=G(n,yn,Δyn),n⩾1 as well as for the existence of monotone solutions of the nonlinear difference equation Δ(an−1(Δyn−1)σ)+knf(yρ(n))=0,n⩾1, where 0<σ=p/q with p even and q odd integers, and some incorrect results in a recent paper are pointed out. Examples which illustrate the importance of our results are also included.