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Stationary solutions of quasi-linear Schrödinger-Poisson systems. (English) Zbl 0909.35133
Summary: 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 solution of a nonlinear Schrödinger-Poisson eigenvalue problem. \(\copyright\) Academic Press.

MSC:
35Q60 PDEs in connection with optics and electromagnetic theory
78A35 Motion of charged particles
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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