Analytic solutions of general nonlinear functional equations near resonance
type: Item
instance of: scholarly article
title: Analytic solutions of general nonlinear functional equations near resonance
zbMATH Open document ID: 1149.39014
author: Bing Xu
author: Weinian Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-04-06T00:00:00Z
review text: The method of majorant series is used to find the unique solution \(\varphi:\mathbb C \to\mathbb C\) which is analytic in a neighborhood of the origin of a \(q\)-difference-type functional equation of infinite order (with inner linear functions having different coefficients \(q_j\)). Applications to \(q\)-difference equations (special cases of those considered in the paper, with \(q_j = q^j\)) as well as to functional equations with iterates of the unknown function are discussed. Results obtained by \textit{E. N. Petropoulou} and \textit{P. D. Siafarikas} [J. Math. Anal. Appl. 279, No. 2, 451--462 (2003; Zbl 1021.39011)] for another special case of the authors' equation are commented and sometimes corrected.
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 39A13
Mathematics Subject Classification ID: 39B32
zbMATH DE Number: 5017404
zbMATH Keywords: functional equations of infinite order
zbMATH Keywords: analytic solutions
zbMATH Keywords: Diophantine condition
zbMATH Keywords: majorant series
zbMATH Keywords: \(q\)-difference equations
zbMATH Keywords: iterative functional equations
reviewed by: Bogdan A. Choczewski
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.05.037
OpenAlex ID: W2037360850
cites work: Q4146134
cites work: Q5604772
cites work: Q5592596
cites work: Invariant curves for planar mappings
cites work: Existence and uniqueness of solutions in \(H_{1}(\Delta)\) of a general class of non-linear functional equations
cites work: About the growth of entire functions solutions of linear algebraic \(q\)- difference equations
cites work: ANALYTIC SOLUTIONS OF A POLYNOMIAL-LIKE ITERATIVE FUNCTIONAL EQUATION
cites work: Analytic solutions of a functional equation for invariant curves
cites work: Analytic solutions of a nonlinear iterative equation near neutral fixed points and poles
cites work: Analytic Solutions of aq-Difference Equation and Applications to Iterative Equations*
cites work: Q3278300
cites work: Discussion on the differentiable solutions of the iterated equation
cites work: Solutions of equivariance for a polynomial-like iterative equation
DOI: 10.1016/J.JMAA.2005.05.037
description: scientific article; zbMATH DE number 5017404