Oscillation of third-order nonlinear delay difference equations

Abstract

Third-order nonlinear difference equations of the form Δ(c nΔ(d nΔx n)) + p nΔx n+1 + q nf(x n-σ) = 0, n ≥ n0 are considered. Here, {c n}, {d n}, {p n}, and {q n} are sequences of positive real numbers for n0 ∈ N, f is a continuous function such that f (u)/u ≥K >0 for u ≠ 0. By means of a Riccati transformation technique we obtain some new oscillation criteria. Examples are given to illustrate the importance of the results. © TÜBİTAK.