In this paper we are dealing with a Schroedinger–Maxwell system in a bounded domain of R^3; the unknowns are the charged standing waves in equilibrium with a purely electrostatic potential. 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 for u. Under mild assumptions involving F and the function q, 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.
Constrained Schroedinger-Poisson System with Non Constant Interaction
PISANI, Lorenzo;SICILIANO GAETANO
2013-01-01
Abstract
In this paper we are dealing with a Schroedinger–Maxwell system in a bounded domain of R^3; the unknowns are the charged standing waves in equilibrium with a purely electrostatic potential. 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 for u. Under mild assumptions involving F and the function q, 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
