On the existence of a solution for elliptic system related to the Maxwell–Schrödinger equations

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On the Schrödinger-Maxwell equations under the effect of a general nonlinear term (2009, background): “Indeed a similar system arises in many mathematical physics contexts, such as in quantum electrodynamics, to describe the interaction between a charge particle interacting with the electromagnetic field, and also in semiconductor theory, in nonlinear optics and in plasma physics.”
Schrodinger-Poisson system with steep potential well (2009, background): “1) has been discussed for different ranges of p, for examples, [9] [10] [12] for p ∈ [3, 5), [4] for p ∈ (2, 5), [16] for p ∈ [2, 3) and [2] [17][3] for p ∈ (1, 5) or general nonlinearity, etc.”
Existence of least energy nodal solution for a Schrödinger–Poisson system in bounded domains (2013, background): “[19] H. Kikuchi, On the existence of a solution for elliptic system related to the Maxwell-Schrödinger equations, Nonlinear Anal.”