On analogies between nonlinear difference and differential equations
type: Item
instance of: scholarly article
title: On analogies between nonlinear difference and differential equations
zbMATH Open document ID: 1207.34118
author: Chungchun Yang
author: Ilpo Laine
published in: Proceedings of the Japan Academy. Series A
publication date: 2010-04-08T00:00:00Z
review text: The authors study some similarities between results on the existence and uniqueness of finite order entire solutions of nonlinear differential equations and difference-differential equations of the form \[ f^n + L(z, f) = h, \] where \(n \geq 2\) is an integer, \(h\) is a given non-vanishing meromorphic function of finite order, and \(L (z, f)\) is a linear difference-differential polynomials, with small meromorphic functions as coefficients. The authors prove for example the following theorem: Theorem 1. Let \(p, q\) be polynomials. Then the nonlinear difference equation \[ f^2 (z) + q (z) f (z +1)=p(z) \] has no transcendental entire solutions of finite order.
Mathematics Subject Classification ID: 34M05
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 5690867
zbMATH Keywords: difference-differential polynomial
zbMATH Keywords: difference polynomial
zbMATH Keywords: difference-differential equation
zbMATH Keywords: Nevanlinna theory
reviewed by: A. Yu. Timofeev
MaRDI profile type: Publication
full work available at URL: pjaa.86.10
OpenAlex ID: W1964967626
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DOI: 10.3792/PJAA.86.10
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description: scientific article; zbMATH DE number 5690867