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Publication Date:
November 2005
ISSN:
1435-5345
DOI:
10.1515/crll.2005.2005.583.29

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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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Rank 37 out of 288 in category Mathematics in the 2011 Thomson Reuters Journal Citation Report/Science Edition
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The Dirichlet boundary value problem for real solutions of the first Painlevé equation on segments in non-positive semi-axis

N. Joshi1 / A. V. Kitaev2

1.

2.

Citation Information: Journal für die reine und angewandte Mathematik. Volume 2005, Issue 583, Pages 29–86, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crll.2005.2005.583.29, November 2005

Publication History:
Received:
13. März 2003
Published Online:
2005-11-07

Abstract

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) = y 0, y(b) = y 0 for a < b ≦ 0.

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