Growth estimates for meromorphic solutions of higher order algebraic differential equations

Shamil Makhmutov, Jouni Rattya, Toni Vesikko

Research output: Contribution to journalArticlepeer-review

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 classXXof meromorphic functions in the unit disc, defined by means of the spherical derivative, andm∈N\{1}m∈N\{1},fm∈Xfm∈Ximpliesf∈Xf∈X. An affirmative answer to this is given for example in the case ofUBCUBC, theαα-normal functions withα≥1α≥1and certain (sufficiently large) Dirichlet type classes,.

Original languageEnglish
Pages (from-to)621-629
Number of pages9
JournalTohoku Mathematical Journal
Volume72
Issue number4
DOIs
Publication statusPublished - Dec 2020
Externally publishedYes

Keywords

  • Complex differential equations
  • Normal functions
  • Spherical derivative

ASJC Scopus subject areas

  • Mathematics(all)

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