GROWTH ESTIMATES FOR MEROMORPHIC SOLUTIONS OF HIGHER ORDER ALGEBRAIC DIFFERENTIAL EQUATIONS

被引：0

作者：

Makhmutov, Shamil ^{[1
]}

Rattya, Jouni ^{[2
]}

Vesikko, Toni ^{[2
]}

机构：

[1] Sultan Qaboos Univ, POB 36,Pc 123, Muscat, Oman

[2] Univ Eastern Finland, POB 111, Joensuu 80101, Finland

来源：

TOHOKU MATHEMATICAL JOURNAL | 2020年 / 72卷 / 04期

关键词：

Complex differential equations; spherical derivative; normal functions;

D O I：

10.2748/tmj.20191118

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 is an element of N \ {1}, f(m) is an element of X implies f is an element of X. An affirmative answer to this is given for example in the case of UBC, the a-normal functions with alpha >= 1 and certain (sufficiently large) Dirichlet type classes.

引用

页码：621 / 629

页数：9

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