Asymptotic and oscillatory behavior of solutions of general nonlinear difference equations of second order

The asymptotic and oscillatory behavior of solutions of some general second-order nonlinear difference equations of the form Δ(anh(yn+1)Δyn)+pnΔyn+qn+1f(yσ(n+1))=0,n Z is studied. Oscillation criteria for their solutions, when “pn” is of constant sign, are established. Results are also presented for the damped-forced equation Δ(anh(yn+1)Δyn)+pnΔyn+qn+1f(yσ(n+1))=en,n Z Examples are inserted in the text for illustrative purposes.