On solutions of linear differential equations of arbitrary fast growth in the unit disc 

Author 
semochkons@ukr.net
Ivan Franko National University of Lviv

Abstract 
We investigate fast growing solutions of linear differential equations in the unit disc. For that we introduce a general scale to measure the growth of functions of infinite order including arbitrary fast growth. We describe the growth relations between entire coefficients and solutions of the linear differential equation $f^{(n)}+a_{n1}(z)f^{(n1)}+\ldots +a_{0}(z)f=0$ in this scale and we investigate the growth of solutions where the coefficient of $f$ dominates the other coefficients near a point on the boundary of the unit disc.

Keywords 
linear differential equation; growth of solutions; Nevanlinna characteristic; iterated order;
meromorphic function

DOI 
doi:10.15330/ms.45.1.311

Reference 
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Pages 
311

Volume 
45

Issue 
1

Year 
2016

Journal 
Matematychni Studii

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