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Zbl 1080.34012
Joshi, N.; Kitaev, A.V.
The Dirichlet boundary value problem for real solutions of the first Painlavé equation on segments in non-positive semi-axis. (English)
[J] J. Reine Angew. Math. 583, 29-86 (2005). ISSN 0075-4102; ISSN 1435-5345/e

The authors study the first Painlevé equation $y''= 6y^2- x$. For this equation, the Dirichlet boundary value problem for real solutions is considered. A complete discussion is presented. Numerical aspects are investigated.
[Lech Górniewicz (Toruń)]

MSC 2000:: *34B30 Special ODE
34B15 Nonlinear boundary value problems of ODE
34A34 Nonlinear ODE and systems, general
34M55 Painlevé and other special equations

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