Asymptotic behavior of third order delay difference equations with a negative middle term

• Main Authors: S. H. Saker, S. Selvarangam, S. Geetha, E. Thandapani, J. Alzabut
• Format: Article
• Language: English
• Published: SpringerOpen 2021-05-01
• Series: Advances in Difference Equations
• Subjects: Third order delay difference equations; Comparison method; Oscillation; Nonoscillation
• Online Access: https://doi.org/10.1186/s13662-021-03407-8

Abstract In this paper, we establish some sufficient conditions which ensure that the solutions of the third order delay difference equation with a negative middle term Δ ( a n Δ ( Δ w n ) α ) − p n ( Δ w n + 1 ) α − q n h ( w n − l ) = 0 , n ≥ n 0 , $$ \Delta \bigl(a_{n}\Delta (\Delta w_{n})^{\alpha } \bigr)-p_{n}(\Delta w_{n+1})^{ \alpha }-q_{n}h(w_{n-l})=0,\quad n\geq n_{0}, $$ are oscillatory. Moreover, we study the asymptotic behavior of the nonoscillatory solutions. Two illustrative examples are included for illustration.