TY - JOUR

T1 - Growth estimates for meromorphic solutions of higher order algebraic differential equations

AU - Makhmutov, Shamil

AU - Rattya, Jouni

AU - Vesikko, Toni

N1 - Publisher Copyright:
© 2020 Tohoku University, Mathematical Institute. All rights reserved.

PY - 2020/12

Y1 - 2020/12

N2 - 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,.

AB - 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,.

KW - Complex differential equations

KW - Normal functions

KW - Spherical derivative

UR - http://www.scopus.com/inward/record.url?scp=85103239574&partnerID=8YFLogxK

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U2 - 10.2748/tmj.20191118

DO - 10.2748/tmj.20191118

M3 - Article

AN - SCOPUS:85103239574

SN - 0040-8735

VL - 72

SP - 621

EP - 629

JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

IS - 4

ER -