Linear third-order difference equations: oscillatory and asymptotic behavior
type: Item
instance of: scholarly article
title: Linear third-order difference equations: oscillatory and asymptotic behavior
zbMATH Open document ID: 0768.39004
author: Yanyan Li
published in: Rocky Mountain Journal of Mathematics
publication date: 1993-06-29T00:00:00Z
review text: A point of contact of the graph of \(U = \{U_ n\}\) satisfying (1) \(\Delta^ 3U_ n + P_{n+1}\Delta U_{n+2} + Q_ nU_{n+2} = 0\), with the real axis is a node. A solution of (1) is said to be oscillatory if it has arbitrarily large nodes. It is proved that (1) always has an oscillatory solution. A sufficient condition is also given in terms of \(P_ n\) and \(Q_ n\) so that (1) has a solution satisfying, \(\text{Sgn }U_ n = \text{Sgn }\Delta U_ n = \text{Sgn }\Delta^ 2U_ n\).
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 219352
zbMATH Keywords: linear third-order difference equations
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: point of contact
zbMATH Keywords: graph
zbMATH Keywords: oscillatory solution
reviewed by: B. M. Agrawal
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072673
OpenAlex ID: W2061958888
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DOI: 10.1216/RMJM/1181072673
description: scientific article; zbMATH DE number 219352