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Entire Solutions of Binomial Differential Equations

Entire Solutions of Binomial Differential Equations We find explicit forms for all the entire solutions of a certain type of non-linear binomial differential equation. This has connections to results of Hayman, Mues, Langley and Bergweiler. Observations about entire solutions of two similar types of binomial differential equations are discussed, and open questions about all three types of equations are posed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Entire Solutions of Binomial Differential Equations

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-021-00384-7
Publisher site
See Article on Publisher Site

Abstract

We find explicit forms for all the entire solutions of a certain type of non-linear binomial differential equation. This has connections to results of Hayman, Mues, Langley and Bergweiler. Observations about entire solutions of two similar types of binomial differential equations are discussed, and open questions about all three types of equations are posed.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Dec 1, 2021

Keywords: Entire function; Non-linear differential equation; Binomial differential equation; Meromorphic function; Nevanlinna theory; 34M10; 34M05; 30D35

References