Comparison results and linearized oscillations for higher-order difference equations

G. Ladas and C. Qian

International Journal of Mathematics and Mathematical Sciences, 1992, vol. 15, 1-14

Abstract:

Consider the difference equations Δ m x n + ( − 1 ) m + 1 p n f ( x n − k ) = 0 , n = 0 , 1 , … ( 1 ) and Δ m y n + ( − 1 ) m + 1 q n g ( y n − ℓ ) = 0 , n = 0 , 1 , … . ( 2 ) We establish a comparison result according to which, when m is odd, every solution of Eq.(1) oscillates provided that every solution of Eq.(2) oscillates and, when m is even, every bounded solution of Eq.(1) oscillates provided that every bounded solution of Eq.(2) oscillates. We also establish a linearized oscillation theorem according to which, when m is odd, every solution of Eq.(1) oscillates if and only if every solution of an associated linear equation Δ m z n + ( − 1 ) m + 1 p z n − k = 0 , n = 0 , 1 , … ( * ) oscillates and, when m is even, every bounded solution of Eq.(1) oscillates if and only if every bounded solution of (*) oscillates.

Date: 1992
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/15/412938.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/15/412938.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:412938

DOI: 10.1155/S0161171292000152

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().