International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 69562, 10 pages

On the asymptotics of the real solutions to the general sixth Painlevé equation

Huizeng Qin1 and Youmin Lu2

1Department of Mathematics and Information Science, Shandong University of Technology, ZiBo, Shandong 255049, China
2Department of Mathematics and Computer Science, Bloomsburg University, Bloomsburg 17815, PA, USA

Received 9 May 2006; Revised 3 September 2006; Accepted 1 October 2006

Copyright © 2006 Huizeng Qin and Youmin Lu. 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.


We study the general sixth Painlevé equation, develop, and justify the existence of several groups of asymptotics of its real solutions. Our methods also justify the differentiability of the asymptotics. Particular attention is paid to the solutions between 0 and 1. We find the asymptotics of all real solutions between 0 and 1 of the sixth Painlevé equation as x+.