Stationary Solutions of Quasi-Linear Schrödinger–Poisson Systems

We show that a high-field version of the periodic Schrödinger–Poisson system including nonlinear terms in the Poisson equation (corresponding to a field-dependent dielectric constant) and effective potentials in the Schrödinger equation has an infinite number of different stationary states which correspond to solutions of a nonlinear Schrödinger–Poisson eigenvalue problem.