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arXiv · 1108.2188

Sub-normal Solutions to Painleve's Second Differential Equation

Norbert Steinmetz
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Abstract

In a recent paper, Aimo Hinkkanen and Ilpo Laine proved that the transcendental solutions to Painleve's second differential equation w"=a+zw+w^3 have either order of growth 3 or else 3/2. We complete this result by proving that there exist no sub-normal solutions (order of growth 3/2) other than the so-called Airy solutions.

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Norbert Steinmetz. 2011-08-10. Sub-normal Solutions to Painleve's Second Differential Equation. https://doi.org/10.1112/blms%2Fbds073

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