Oscillation of third-order nonlinear delay difference equations

Authors

MUSTAFA FAHRİ AKTAŞ
AYDIN TİRYAKİ
AĞACIK ZAFER

DOI

10.3906/mat-1010-67

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

First Page

422

Last Page

436

Recommended Citation

AKTAŞ, MUSTAFA FAHRİ; TİRYAKİ, AYDIN; and ZAFER, AĞACIK (2012) "Oscillation of third-order nonlinear delay difference equations," Turkish Journal of Mathematics: Vol. 36: No. 3, Article 8. https://doi.org/10.3906/mat-1010-67
Available at: https://journals.tubitak.gov.tr/math/vol36/iss3/8