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On Finite-Order Meromorphic Solutions of a Class Containing a Difference Painlevé I Equation

On Finite-Order Meromorphic Solutions of a Class Containing a Difference Painlevé I Equation In this article, we investigate the growth and value distribution of finite-order transcendental meromorphic solutions for some non-linear difference equations. For instance, we show that demanding the existence of a transcendental meromorphic solution of a large class of difference equations containing difference Painlevé I reduces the class either to a smaller one which still contains the difference Painlevé I, or to a class of first-order equations. In addition, for certain classes of equations, we prove the existence of rational solutions and give their forms. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

On Finite-Order Meromorphic Solutions of a Class Containing a Difference Painlevé I Equation

Computational Methods and Function Theory , Volume 13 (4) – Nov 28, 2013

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Publisher
Springer Journals
Copyright
Copyright © 2013 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-013-0044-9
Publisher site
See Article on Publisher Site

Abstract

In this article, we investigate the growth and value distribution of finite-order transcendental meromorphic solutions for some non-linear difference equations. For instance, we show that demanding the existence of a transcendental meromorphic solution of a large class of difference equations containing difference Painlevé I reduces the class either to a smaller one which still contains the difference Painlevé I, or to a class of first-order equations. In addition, for certain classes of equations, we prove the existence of rational solutions and give their forms.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Nov 28, 2013

References