Guedda, Mohammed Note on the uniqueness of a global positive solution to the second Painlevé equation. (English) Zbl 0983.34082 Electron. J. Differ. Equ. 2001, Paper No. 49, 4 p. (2001). Summary: 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, B. Helfer and F. B. Weissler [Eur. J. Appl. Math. 9, No. 3, 223-243 (1998; Zbl 0920.34051)]have found a unique solution. The author shows that, without any assumption at infinity, this problem has exactly one global positive solution. Moreover, the solution behaves like \(\sqrt{t}\) as \(t\) approaches infinity. Cited in 2 Documents MSC: 34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies 34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain 34B15 Nonlinear boundary value problems for ordinary differential equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 82D55 Statistical mechanics of superconductors Keywords:second Painlevé equation; Neumann condition; global existence Citations:Zbl 0920.34051 PDFBibTeX XMLCite \textit{M. Guedda}, Electron. J. Differ. Equ. 2001, Paper No. 49, 4 p. (2001; Zbl 0983.34082) Full Text: EuDML EMIS