Journals / Turkish Journal of Mathematics / 2012 / Cilt: 36 - Sayı: 3
Oscillation of third-order nonlinear delay difference equations
- Pages
- 422–436
- DOI
- —
Abstract
Third-order nonlinear difference equations of the form D (cnD (dnD xn))+pnD xn+1+qnf(xn-s)=0, n\geq n0 are considered. Here, {cn}, {dn}, {pn}, and {qn} are sequences of positive real numbers for n0 \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.
Özet
Third-order nonlinear difference equations of the form D (cnD (dnD xn))+pnD xn+1+qnf(xn-s)=0, n\geq n0 are considered. Here, {cn}, {dn}, {pn}, and {qn} are sequences of positive real numbers for n0 \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.