Standing waves for a gauged nonlinear Schr\"{o}dinger equation with a vortex point

TL;DR

This paper investigates radial stationary states of a gauged nonlinear Schrödinger equation with a vortex point, analyzing the variational structure and extending known results for the non-regular case in two dimensions.

Contribution

It extends the analysis of stationary states for gauged nonlinear Schrödinger equations to include vortex points, revealing new insights into their variational properties.

Findings

Analysis of the global behavior of the associated functional

Extension of known results to the vortex case

Characterization of stationary states with vortex at the origin

Abstract

This paper is motivated by a gauged Schr\"{o}dinger equation in dimension 2. We are concerned with radial stationary states under the presence of a vortex at the origin. Those states solve a nonlinear nonlocal PDE with a variational structure. We will study the global behavior of that functional, extending known results for the regular case.