Note on the Uniqueness of a Global Positive Solution to the Second Painleve Equation
Date
2001-07-09
Authors
Guedda, Mohammed
Journal Title
Journal ISSN
Volume Title
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.