CONSTRAINED SCHRODINGER-POISSON SYSTEM WITH NON-CONSTANT INTERACTION

In this paper we are dealing with a Schrodinger-Maxwell system in a bounded domain of R-3; the unknowns are the charged standing waves psi = e-(i omega t)u(x) in equilibrium with a purely electrostatic potential phi. 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 phi 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 L-2 for 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. (AU)