Nonautonomous Klein–Gordon–Maxwell systems in a bounded domain

This paper deals with the Klein–Gordon–Maxwell system in a bounded spatial domain with a nonuniform coupling. We discuss the existence of standing waves in equilibrium with a purely electrostatic field, assuming homogeneous Dirichlet boundary conditions on the matter field and nonhomogeneous Neumann boundary conditions on the electric potential. Under suitable conditionswe prove existence and nonexistence results. Since the system is variational, we use Ljusternik–Schnirelmann theory.