On the oscillatory behaviour of solutions of second order nonlinear difference equations
type: Item
instance of: scholarly article
title: On the oscillatory behaviour of solutions of second order nonlinear difference equations
zbMATH Open document ID: 0803.39004
DOI: 10.4171/ZAA/509
author: S. Pandian
author: E. Thandapani
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1995-01-02T00:00:00Z
review text: The authors consider the difference equation (1) \(\Delta (a_ n \Delta y_ n) + q_{n + 1} f(y_{n + 1}) = r_ n\), \(n \in N_ 0\). All values in (1) are real. A solution \(\{y_ n\}\) of (1) is said to be oscillatory if it is neither essentially positive nor essentially negative. Sufficient conditions for the solution \(\{y_ n\}\) of (1) to be oscillatory or \(\liminf_{n \to \infty} | y_ n | = 0\) are established. Sufficient conditions for oscillation of all solutions of equation (1) when \(r_ n = 0\) for all \(n \in N_ 0\) are obtained.
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 605112
zbMATH Keywords: second order nonlinear difference equations
zbMATH Keywords: oscillatory solutions
reviewed by: Victor I. Tkachenko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 605112