Justification of an asymptotic expansion at infinity

TL;DR

This paper proves the existence of exact solutions to a system of ordinary differential equations that match a given family of asymptotic solutions at infinity.

Contribution

It establishes the existence of solutions with specified asymptotic behavior at infinity for a class of ODE systems.

Findings

Existence of solutions with prescribed asymptotics at infinity

Construction of asymptotic solutions for ODE systems

Mathematical proof of solution existence

Abstract

A family of asymptotic solutions at infinity for the system of ordinary differential equations is considered. Existence of exact solutions which have these asymptotics is proved.