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2020 Growth estimates for meromorphic solutions of higher order algebraic differential equations
Shamil Makhmutov, Jouni Rättyä, Toni Vesikko
Tohoku Math. J. (2) 72(4): 621-629 (2020). DOI: 10.2748/tmj.20191118

Abstract

We establish pointwise growth estimates for the spherical derivative of solutions of the first order algebraic differential equations. A generalization of this result to higher order equations is also given. We discuss the related question of when for a given class $X$ of meromorphic functions in the unit disc, defined by means of the spherical derivative, and $m\in \mathbb{N}\setminus\{1\}$, $f^m\in X$ implies $f\in X$. An affirmative answer to this is given for example in the case of $\mathord{\rm UBC}$, the $\alpha$-normal functions with $\alpha\ge 1$ and certain (sufficiently large) Dirichlet type classes.

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Shamil Makhmutov. Jouni Rättyä. Toni Vesikko. "Growth estimates for meromorphic solutions of higher order algebraic differential equations." Tohoku Math. J. (2) 72 (4) 621 - 629, 2020. https://doi.org/10.2748/tmj.20191118

Information

Published: 2020
First available in Project Euclid: 22 December 2020

MathSciNet: MR4194190
Digital Object Identifier: 10.2748/tmj.20191118

Subjects:
Primary: 34M05
Secondary: 30D45

Rights: Copyright © 2020 Tohoku University

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Vol.72 • No. 4 • 2020
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