Existence and blow-up of attractive Gross-Pitaevskii minimizers with general bounded potentials

TL;DR

This paper investigates the existence and blow-up behavior of minimizers in the 2D attractive Gross-Pitaevskii functional under bounded potentials as interaction strength approaches a critical value.

Contribution

It establishes existence and blow-up results for minimizers with general bounded external potentials in the 2D attractive Gross-Pitaevskii model.

Findings

Existence of minimizers under certain conditions.

Blow-up behavior as interaction strength approaches critical value.

Results valid for all bounded external potentials satisfying general assumptions.

Abstract

The paper is concerned with the existence and blow-up behavior of the minimizers for the 2D attractive Gross-Pitaevskii functional when the interaction strength increases to a critical value. Our results hold for all bounded external potential satisfying some general assumptions.