86 research outputs found
Sub-normal Solutions to Painleve's Second Differential Equation
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
Reminiscence Of An Open Problem: Remarks On Nevanlinna's Four-Value-Theorem
The aim of this paper is to describe the origin, first solutions, further
progress, the state of art, and a new ansatz in the treatment of a problem
dating back to the 1920's, which still has not found a satisfactory solution
and deserves to be better known
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