Meromorphic solutions on the first order non-linear difference equations
type: Item
instance of: scholarly article
title: Meromorphic solutions on the first order non-linear difference equations
zbMATH Open document ID: 1463.30151
author: Jun Li
author: Kefeng Liu
published in: Analysis Mathematica
publication date: 2020-10-02T00:00:00Z
review text: In the paper the authors consider the first order nonlinear difference equation of the form \[C(z, f)f^{2}(z + c) + B(z, f) f(z + c) + A(z, f) = 0,\] where \(A(z, f)\), \(B(z, f)\) and \(C(z, f)\) are polynomials in \(f\) with rational coefficients. Let \(t = \deg_{f}A(z, f)\), \(n = \deg_{f}B(z, f)\) and \(m = \deg_{f}C(z, f)\). A typical result of the paper states that if the above equation admits transcendental entire solution \(f\) with hyper-order less than \(1\), then \(m \leq \max \{n - 1, t - 2\}\), \(n \leq \max \{m + 1, t - 1\}\) and \(t \leq \max\{m + 2, n + 1\}\).
reviewed by: Indrajit Lahiri
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 39B32
zbMATH DE Number: 7254986
zbMATH Keywords: meromorphic solution
zbMATH Keywords: difference equation
zbMATH Keywords: value distribution
zbMATH Keywords: hyper-order
MaRDI profile type: Publication
full work available at URL: s10476-020-0032-z
OpenAlex ID: W3024028092
cites work: On a Class of Meromorphic Functions
cites work: On the Nevanlinna characteristic of \(f(z+\eta)\) and difference equations in the complex plane
cites work: On Integral and Meromorphic Functions
cites work: On the equation \(f^n(z) + g^n(z) = E^{ \alpha z+ \beta }\)
cites work: Difference analogue of the lemma on the logarithmic derivative with applications to difference equations
cites work: Holomorphic curves with shift-invariant hyperplane preimages
cites work: Q5723337
cites work: Clunie theorems for difference and q -difference polynomials
cites work: Difference analogue of Cartan's second main theorem for slowly moving periodic targets
cites work: A note on a difference analogue of the Valiron-Mohon'ko theorem
cites work: Q4614832
cites work: Meromorphic solutions of certain difference equations of first order
cites work: On the Fermat-type equation \({f^3(z)+f^3(z+c)=1}\)
cites work: Ein Malmquistscher Satz für algebraische Differentialgleichungen erster Ordnung.
cites work: Q4827955
cites work: Existence of meromorphic solutions of first-order difference equations
DOI: 10.1007/S10476-020-0032-Z
description: scientific article; zbMATH DE number 7254986