Long-Time Dynamics of the Schrödinger–Poisson–Slater System

In this paper we analyze the asymptotic behaviour of solutions to the Schrödinger–Poisson–Slater (SPS) system in the frame of semiconductor modeling. Depending on the potential energy and on the physical constants associated with the model, the repulsive SPS system develops stationary or periodic solutions. These solutions preserve the L ^p (?³) norm or exhibit dispersion properties. In comparison with the Schrödinger–Poisson (SP) system, only the last kind of solutions appear.