On the growth of solutions of 𝑓”+𝑔𝑓’+ℎ𝑓=0

Hellerstein, Simon; Miles, Joseph; Rossi, John

doi:10.1090/S0002-9947-1991-1005080-X

On the growth of solutions of $f”+gf’+hf=0$
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by Simon Hellerstein, Joseph Miles and John Rossi PDF

Trans. Amer. Math. Soc. 324 (1991), 693-706 Request permission

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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