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

Advances in Difference Equations

article

Saker, S. H.¹  Selvarangam, S.³  Geetha, S.³  Thandapani, E.⁴  Alzabut, J.⁵ 

[1] Department of Mathematics, Faculty of Science, Galala University;Department of Mathematics, Faculty of Science, Mansoura University;Department of Mathematics, Presidency College (Autonomous);Ramanujan Institute for Advanced Study in Mathematics, University of Madras;Department of Mathematics and General Sciences, Prince Sultan University;Group of Mathematics, Faculty of Engineering, Ostim Technical University

关键词: Third order delay difference equations;    Comparison method;    Oscillation;    Nonoscillation;   

DOI  :  10.1186/s13662-021-03407-8

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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$$ \Delta \bigl(a_{n}\Delta (\Delta w_{n})^{\alpha } \bigr)-p_{n}(\Delta w_{n+1})^{ \alpha }-q_{n}h(w_{n-l})=0,\quad n\geq n_{0}, $$ are oscillatory. Moreover, we study the asymptotic behavior of the nonoscillatory solutions. Two illustrative examples are included for illustration.

【 授权许可】

CC BY