On the solvability of a linear inhomogeneous problem arising in the blow-up analysis of the phase separation in Bose-Einstein condensates

TL;DR

This paper investigates the solvability of a linear inhomogeneous problem that appears in the detailed asymptotic analysis of wave functions in multi-component Bose-Einstein condensates, focusing on phase separation phenomena.

Contribution

It provides new insights into the solvability conditions of the linear system relevant to the asymptotic expansion in Bose-Einstein condensates with segregation.

Findings

Established solvability criteria for the linear system.

Analyzed the behavior of wave functions near the interface.

Contributed to the mathematical understanding of phase separation in condensates.

Abstract

We study the inhomogeneous linear system which arises in the higher order asymptotic expansion of the wave functions of multi-component Bose-Einstein condensates, across the regular part of the interface, in the case of segregation.