Sub-normal Solutions to Painleve's Second Differential Equation

Details Sub-normal Solutions to Painleve's Second Differential Equation Sub-normal Solutions to Painleve's Second Differential Equation

2011-08-10

arxiv.org/abs/1108.2188v1

Mathematics

Complex Variables

Scientific paper

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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