Concentration on circles for nonlinear Schr\"odinger-Poisson systems with unbounded potentials vanishing at infinity

TL;DR

This paper proves the existence of solutions that concentrate on a circle for nonlinear Schrödinger-Poisson systems with unbounded potentials that vanish at infinity, using a variational method.

Contribution

It introduces a variational approach to establish solutions concentrating on a circle in complex potential landscapes.

Findings

Solutions concentrate on a circle

Applicable to systems with unbounded potentials

Uses variational methods

Abstract

The present paper is devoted to weighted Nonlinear Schr\"odinger- Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, we prove the existence of solutions concentrating on a circle.