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arXiv · 1906.05761

Growth estimates for meromorphic solutions of higher order algebraic differential equations

Shamil Makhmutov·Jouni Rättyä·Toni Vesikko
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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 $\alpha\ge1$ and certain (sufficiently large) Dirichlet type classes.

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Shamil Makhmutov, Jouni Rättyä, Toni Vesikko. 2019-06-13. Growth estimates for meromorphic solutions of higher order algebraic differential equations. https://arxiv.org/abs/1906.05761

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