Electron. J. Diff. Eqns., Vol. 2001(2001), No. 49, pp. 1-4.

Note on the uniqueness of a global positive solution to the second Painleve equation

Mohammed Guedda

Abstract:
The purpose of this note is to study the uniqueness of solutions to
$ u'' -u^3 + (t-c)u = 0$, for $ t \in (0,+\infty)$
with Neumann condition at 0. Assuming a certain conditon at infinity, Helfer and Weissler [6] have found a unique solution. We show that, without any assumptions at infinity, this problem has exactly one global positive solution. Moreover, the solution behaves like $\sqrt{t}$ as $t$ approaches infinity.

Submitted February 08, 2001. Published July 9, 2001.
Math Subject Classifications: 34B15, 35B05, 82D55.
Key Words: Second Painleve equation, Neumann condition, global existence.

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Mohammed Guedda
Universite de Picardie Jules Verne
Faculte de Mathematiques et d'Informatique
33, rue Saint-Leu 80039 Amiens, France
e-mail: Guedda@u-picardie.fr

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