Conditions for the oscillation of solutions of iterative equations
type: Item
instance of: scholarly article
title: Conditions for the oscillation of solutions of iterative equations
zbMATH Open document ID: 1071.39025
DOI: 10.1155/S1085337504306305
author: W. Nowakowska
author: J. Werbowski
published in: Abstract and Applied Analysis
publication date: 2005-04-29T00:00:00Z
full work available at URL: https://eudml.org/doc/51637
review text: While the problem of oscillation of solutions of differential and difference equations has received a lot of attention, such problem has not been faced for many classes of functional equations in a single variable. The authors of this paper deal with such problems in the case of the linear iterative functional equation of the form: \[ \sum_{i=0}^{m+1} Q_i (t) x (g^i (t)) = 0, \quad m \geq 1 , \] where \(x\) is an unknown real-valued function and \(Q_i : I \to R \), \( i=0,\dots,m+1\) and \( g: I \to I \) are given functions (where \(I\) is an unbounded subset of \([0, \infty) \) and \( g^i \) means the ith iterate of \( g \), \( g^0 = j \), \(g^{i+1} = g \circ g^i\)). Under some natural regular conditions the existence of oscillatory solutions is proven.
reviewed by: Claudi Alsina
Mathematics Subject Classification ID: 39B12
zbMATH DE Number: 2163672
zbMATH Keywords: oscillation of solutions
zbMATH Keywords: linear iterative functional equation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2163672