Note on a Schrödinger–Poisson system in a bounded domain

This work is concerned with a nonlinear system of Schrödinger–Poisson equations in a bounded domain with Dirichlet boundary conditions. We prove the existence of infinitely many solutions u(x)e−iωt, for every value of ωω, in equilibrium with the electrostatic field ϕ(x)ϕ(x).