Oscillation of third-order nonlinear delay difference equations

Authors: MUSTAFA FAHRİ AKTAŞ, AYDIN TİRYAKİ, AĞACIK ZAFER

Abstract: Third-order nonlinear difference equations of the form \Delta (c_n\Delta (d_n\Delta x_n))+p_n\Delta x_{n+1}+q_nf(x_{n-\sigma})=0, n\geq n_{0} are considered. Here, {c_n}, {d_n}, {p_n}, and {q_n} are sequences of positive real numbers for n_0 \in N, f is a continuous function such that f(u) /u\geq K > 0 for u \neq 0. By means of a Riccati transformation technique we obtain some new oscillation criteria. Examples are given to illustrate the importance of the results.

Keywords: Difference equation, Delay, Third order, Oscillation, Nonoscillation, Riccati transformation

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