Nonoscillation and oscillation criteria for class of higher - order difference equations involving generalized difference operator

Authors : Aysun NAR, Yaşar BOLAT, Serbun Ufuk DEĞER, Murat GEVGEŞOĞLU

Pages : 188-203

Doi:10.31801/cfsuasmas.904804

View : 16 | Download : 19

Publication Date : 2022-03-30

Article Type : Research Paper

Abstract :In this paper, sufficient conditions are obtained for nonoscillation/oscillation of all solutions of a class of higher-order difference equations involving the generalized difference operator of the form $\Delta _{a}^{k}insert ignore into journalissuearticles values(p_{n}\Delta _{a}^{2}y_{n});=finsert ignore into journalissuearticles values(n,y_{n},\Delta_{a}y_{n},\Delta _{a}^{2}y_{n},...,\Delta _{a}^{k+1}y_{n});,$ where $\Delta _{a}$ is generalized difference operator which is defined as $\Delta _{a}y_{n}=y_{n+1}-ay_{n}, a\neq{0}.$
Keywords : Difference equations, generalized difference operator, oscillation, nonoscillation