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

Author
N. S. Semochko
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 $f^{(n)}+a_{n-1}(z)f^{(n-1)}+\ldots +a_{0}(z)f=0$ 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.45.1.3-11
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Pages
3-11
Volume
45
Issue
1
Year
2016
Journal
Matematychni Studii
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