Existence of solutions with prescribed frequency for the perturbed Schrödinger-Bopp-Podolsky system in bounded domains

Abstract

In this paper, we show that the Schrödinger-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 Schrödinger 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.

arXiv comment10 pages. Comments are most welcome