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 $\Delta _{a}^{k}(p_{n}\Delta _{a}^{2}y_{n})=f(n,y_{n},\Delta_{a}y_{n},\Delta _{a}^{2}y_{n},...,\Delta _{a}^{k+1}y_{n}),$ where $\Delta _{a}$ is generalized difference operator which is defined as $\Delta _{a}y_{n}=y_{n+1}-ay_{n}, a\neq{0}.$
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Amaç & Hipotez: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 $\Delta _{a}^{k}(p_{n}\Delta _{a}^{2}y_{n})=f(n,y_{n},\Delta_{a}y_{n},\Delta _{a}^{2}y_{n},...,\Delta _{a}^{k+1}y_{n}),$ where $\Delta _{a}$ is generalized difference operator which is defined as $\Delta _{a}y_{n}=y_{n+1}-ay_{n}, a\neq{0}.$
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Temel Bulgular & Veri: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 $\Delta _{a}^{k}(p_{n}\Delta _{a}^{2}y_{n})=f(n,y_{n},\Delta_{a}y_{n},\Delta _{a}^{2}y_{n},...,\Delta _{a}^{k+1}y_{n}),$ where $\Delta _{a}$ is generalized difference operator which is defined as $\Delta _{a}y_{n}=y_{n+1}-ay_{n}, a\neq{0}.$
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Sonuç & Katkı: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 $\Delta _{a}^{k}(p_{n}\Delta _{a}^{2}y_{n})=f(n,y_{n},\Delta_{a}y_{n},\Delta _{a}^{2}y_{n},...,\Delta _{a}^{k+1}y_{n}),$ where $\Delta _{a}$ is generalized difference operator which is defined as $\Delta _{a}y_{n}=y_{n+1}-ay_{n}, a\neq{0}.$
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 $\Delta _{a}^{k}(p_{n}\Delta _{a}^{2}y_{n})=f(n,y_{n},\Delta_{a}y_{n},\Delta _{a}^{2}y_{n},...,\Delta _{a}^{k+1}y_{n}),$ where $\Delta _{a}$ is generalized difference operator which is defined as $\Delta _{a}y_{n}=y_{n+1}-ay_{n}, a\neq{0}.$
Nar, A., Bolat, Y., Değer, S. U., Gevgeşoğlu, M. (2022). Nonoscillation and oscillation criteria for class of higher - order difference equations involving generalized difference operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 71 Issue: 1. https://doi.org/10.31801/cfsuasmas.904804
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