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Licensed Unlicensed Requires Authentication Published by De Gruyter November 7, 2005

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

  • N. Joshi and A. V. Kitaev
From the journal


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.

Published Online: 2005-11-07
Published in Print: 2005-06-27

© Walter de Gruyter

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