Existence of solutions with prescribed frequency for the perturbed Schr\"odinger-Bopp-Podolsky system in bounded domains

TL;DR

This paper proves the existence of infinitely many solutions with prescribed frequency for a perturbed Schr"odinger-Bopp-Podolsky system in bounded domains using variational methods and the Mountain Pass theorem.

Contribution

It establishes the existence of multiple solutions with specific frequencies for the system under general boundary conditions, extending previous results.

Findings

Infinitely many solutions exist for the system.

Solutions can be prescribed with any frequency.

The approach uses a symmetric Mountain Pass theorem.

Abstract

In this paper, we show that the Schr\"odinger-Bopp-Podolsky system with Dirichlet boundary conditions in a bounded domain possesses infinitely many solutions of prescribed frequency, for any set of (continuous) boundary conditions, provided that the Schr\"odinger equation is perturbed with a suitable nonlinearity. Our approach is variational, and our proof is based on a symmetric variant of the Mountain Pass theorem.