Oscillation theorems and existence of positive monotone solutions for second order nonlinear difference equations

Abstract

We offer sufficient conditions for the oscillation of all solutions 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 a positive monotone solution of the damped difference equation Δ(an(Δyn)σ) + bn(Δyn)σ + H(n, yn, Δyn) = 0, n ≥ 0, where 0 < σ = p q with p, q odd integers, or p even and q odd integers. Examples which dwell upon the importance of our results are also included. © 1995.