Note on the Uniqueness of a Global Positive Solution to the Second Painleve Equation

Date

2001-07-09

Authors

Guedda, Mohammed

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Publisher

Southwest Texas State University, Department of Mathematics

Abstract

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 [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 as √t as t approaches infinity.

Description

Keywords

Second Painleve equation, Neumann condition, Global existence

Citation

Guedda, M. (2001). Note on the uniqueness of a global positive solution to the second Painleve equation. <i>Electronic Journal of Differential Equations, 2001</i>(49), pp. 1-4.

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Attribution 4.0 International

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