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

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.