Abstract
In this paper we are dealing with a Schrödinger–Maxwell system in a bounded domain of R3; the unknowns are the charged standing waves ψ = e-iωtu(x) in equilibrium with a purely electrostatic potential ϕ. The system is not autonomous, in the sense that the coupling depends on a function q = q(x). The non-homogeneous Neumann boundary condition on ϕ prescribes the flux of the electric field 𝔉 and gives rise to a necessary condition. On the other hand we consider the usual normalizing condition in L2for u. Under mild assumptions involving 𝔉 and the function q = q(x), we prove that this problem has a variational framework: its solutions can be characterized as constrained critical points. Then, by means of the Ljusternick–Schnirelmann theory, we get the existence of infinitely many solutions.
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