International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 69, Pages 3821-3828
Justification of the existence of a group of asymptotics of the general fifth Painlevé transcendent
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.
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.