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Zbl 1155.34372
Qin, Hui-Zeng; Lu, You-Min
A note on an open problem about the first Painlevé equation. (English)
[J] Acta Math. Appl. Sin., Engl. Ser. 24, No. 2, 203-210 (2008). ISSN 0168-9673; ISSN 1618-3932/e

From the introduction: We study the initial value problem of the first Painlevé equation: $$y''=6y^2+x, \qquad y(0)=\kappa, \quad y'(y)=\mu,$$ and find conditions on $\kappa$ and $\mu$ for this problem to have an oscillating solution. This is an open problem posed by Peter A. Clarkson.

MSC 2000:: *34M55 Painlevé and other special equations
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: first Painlevé equation; oscillating solutions; numerical method

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