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

摘要

There are several existing ways in developing the asymptotics ofthe Painlevé transcendents. But it is always a hard task tojustify the existence of these asymptotics. In this note, weapply the successive approximation to the general fifthPainlevé equation and rigorously prove the existence of agroup of asymptotics of its solutions.