Note on the Uniqueness of a Global Positive Solution to the Second Painleve Equation
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The purpose of this note is to study the uniqueness of solutions to u'' - u3 + (t - c)u = 0, for t ∈ (0, +∞) with Neumann condition at 0. Assuming a certain condition at infinity, Helfer and Weissler  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 as √t as t approaches infinity.
CitationGuedda, M. (2001). Note on the uniqueness of a global positive solution to the second Painleve equation. Electronic Journal of Differential Equations, 2001(49), pp. 1-4.
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