Asymptotics of the nonnegative solutions of the general fifth painlevé equation

Abstract

Asymptotic behaviour of the solutions of the fifth Painlevé transcendent (PV)

where α, β, γ and δ are parameters, have been studied under various conditions on the parameters. In fact, (PV) can be transformed to the Painlevé transcendent (PIII)

where α and β are parameters, under most of these conditions. In this work, we find an asymptotic representation of a group of nonnegative solutions of (PV) as x→0+ and +∞ under very general conditions on the parameters.

Keywords:

• Asymptotics
• analysis
• solutions
• Painlevé equation

AMS:

• 34E99

Additional information

Notes on contributors

Youmin Lu

1

Bryce Mcleod

2