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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the growth of solutions of $ f''+gf'+hf=0$


Authors: Simon Hellerstein, Joseph Miles and John Rossi
Journal: Trans. Amer. Math. Soc. 324 (1991), 693-706
MSC: Primary 30D20; Secondary 34A20
MathSciNet review: 1005080
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Abstract: Suppose $ g$ and $ h$ are entire functions with the order of $ h$ less than the order of $ g$. If the order of $ g$ does not exceed $ \tfrac{1} {2}$, it is shown that every (necessarily entire) nonconstant solution $ f$ of the differential equation $ f'' + gf' + hf = 0$ has infinite order. This result extends previous work of Ozawa and Gundersen.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1005080-X
PII: S 0002-9947(1991)1005080-X
Keywords: Differential equation, entire function, finite order, Nevanlinna characteristic
Article copyright: © Copyright 1991 American Mathematical Society