International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 69, Pages 3821-3828
doi:10.1155/S0161171204402385

Justification of the existence of a group of asymptotics of the general fifth Painlevé transcendent

Youmin Lu1 and Zhoude Shao2

1Department of Mathematics and Computer Science, Bloomsburg University, Bloomsburg 17815, PA, USA
2Department of Mathematics, Millersville University, Millersville 17551, PA, USA

Received 10 February 2004

Copyright © 2004 Youmin Lu and Zhoude Shao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

There are several existing ways in developing the asymptotics of the Painlevé transcendents. But it is always a hard task to justify the existence of these asymptotics. In this note, we apply the successive approximation to the general fifth Painlevé equation and rigorously prove the existence of a group of asymptotics of its solutions.