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

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.