Abstract
In a recent paper devoted to the study of the superheating field attached to a semi-infinite superconductor, Chapman [1] constructs a family of approximate solutions of the Ginzburg–Landau system. This construction, based on a matching procedure, implicitly uses the existence of a family of solutions depending on a parameter c ∈ IR of the Painleve equation in a semi-infinite interval (0, +∞) formula here with a Neumann condition at 0 formula here and having a prescribed behaviour at +∞ formula here In this paper we prove the existence of such a family of solutions and investigate its properties. Moreover, we prove that the second coefficient in Chapman's expansion of the superheating field is finite.
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