Quasi-adjoint third order difference equations: Oscillatory and asymptotic behavior
type: Item
instance of: scholarly article
title: Quasi-adjoint third order difference equations: Oscillatory and asymptotic behavior
zbMATH Open document ID: 0619.39004
DOI: 10.1155/S0161171286000947
author: B. George
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46180
review text: It is shown that the linear difference equation \(\Delta^ 3V_ n+P_{n-1}V_{n+1}=0\) has oscillatory solutions if and only if any non- oscillatory solution \(V_ n\) satisfies the relation \(V_ n\Delta V_ n\Delta^ 2V_ n\neq 0\), \(sgnV_ n=sgn\Delta^ 2V_ n\neq sgn\Delta V_ n\), \(n\geq 1\). This is a discrete analogue of a result of \textit{A. C. Lazer} [Pac. J. Math. 17, 435-466 (1966; Zbl 0143.315)] for the differential equation \(y\prime''+py'+qy=0\). An example is given for an equation of the above form without oscillatory solutions.
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 4004815
zbMATH Keywords: third order
zbMATH Keywords: quasi-adjoint equations
zbMATH Keywords: difference equation
zbMATH Keywords: oscillatory solutions
zbMATH Keywords: non-oscillatory solution
reviewed by: Bernd Aulbach
MaRDI profile type: Publication
OpenAlex ID: W1995293490
description: scientific article; zbMATH DE number 4004815