On solutions of linear differential equations of arbitrary fast growth in the unit disc |
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| Author |
semochkons@ukr.net
Ivan Franko National University of Lviv
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| 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.
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| Keywords |
linear differential equation; growth of solutions; Nevanlinna characteristic; iterated order;
meromorphic function
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| DOI |
doi:10.15330/ms.45.1.3-11
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| Reference |
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| Pages |
3-11
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| Volume |
45
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| Issue |
1
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| Year |
2016
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| Journal |
Matematychni Studii
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| Full text of paper | |
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