Growth estimates for meromorphic solutions of higher order algebraic differential equations

Autor:	Makhmutov, Shamil, Rättyä, Jouni, Vesikko, Toni
Rok vydání:	2019
Předmět:	Mathematics - Complex Variables 34M10 34M05 (Primary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 8 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1906.05761 Zobrazit plný text záznamu View this record from Arxiv