Sub-normal Solutions to Painleve's Second Differential Equation
arXiv:1108.2188 · doi:10.1112/blms/bds073
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.