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N. Joshi, A. V. Kitaev

The Dirichlet boundary value problem for real solutions of the ?rst Painlevé equation on segments in non-positive semi-axis

We develop a qualitative theory for real solutions of the equation y” = 6y ² ? x. In this work a restriction x ? 0 is assumed. An important ingredient of our theory is the introduction of several new transcendental functions of one, two, and three variables that describe different properties of the solutions. In particular, the results obtained allow us to completely analyse the Dirichlet boundary value problem y(a) = y⁰, y(b) = y₀ for a < b ? 0.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2005, 06/2005
Pages: 29 - 86

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