Oscillatory solutions of linear iterative functional equations
type: Item
instance of: scholarly article
title: Oscillatory solutions of linear iterative functional equations
zbMATH Open document ID: 1083.39021
author: W. Nowakowska
author: J. Werbowski
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2005-03-07T00:00:00Z
review text: The authors give three sufficient conditions for the oscillation of all solutions \(x\) of the linear functional equation \[ Q_0(t)x(t)+Q_1(t)x(g(t))+Q_2(t)x(g^2(t))+\dots +Q_{m+1}(t)x(g^{m+1}(t))=0, \] where \(m\) is a fixed positive integer, the functions \(Q_k:I\to \mathbb{R}\) for \(k\in \{0, \dots , m+1\}\), \(g:I\to I\) are given and \(I\) is an unbounded subset of the set of positive reals. These conditions can be applied to recurrence equations if one takes the set of positive integers as \(I\). Moreover, the authors compare their results with known results for the recurrence equation \[ \Delta x(n)=p(n)x(n+2), \] where \(p:\mathbb{N}\to (0,\infty)\).
reviewed by: Zbigniew Leśniak
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 2141194
zbMATH Keywords: iterative equations
zbMATH Keywords: oscillation
zbMATH Keywords: linear functional equations
zbMATH Keywords: recurrence equations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2141194