Sub-normal Solutions to Painleve's Second Differential Equation
Complex Variables
2014-02-26 v1 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.1108.2188,
title = {Sub-normal Solutions to Painleve's Second Differential Equation},
author = {Norbert Steinmetz},
journal= {arXiv preprint arXiv:1108.2188},
year = {2014}
}