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On quasi‐linear Schrödinger–Poisson systems
Author(s) -
Illner R.,
Lange H.,
Toomire B.,
Zweifel Paul
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19970925)20:14<1223::aid-mma911>3.0.co;2-o
Subject(s) - mathematics , uniqueness , poisson distribution , galerkin method , uniqueness theorem for poisson's equation , nonlinear system , mathematical analysis , constant (computer programming) , poisson's equation , matrix (chemical analysis) , field (mathematics) , pure mathematics , quantum mechanics , physics , statistics , materials science , computer science , composite material , programming language
We study a high‐field version of the periodic Schrödinger–Poisson system, for which the Poisson equation includes nonlinear terms corresponding to a field‐dependent dielectric constant. Using a Galerkin scheme, we prove global existence and uniqueness, and present the matrix equations for the numerical evaluation of the potential. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.