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
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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 -