Non-radially symmetric solutions of nonlinear Schrödinger equation coupled with Maxwell equations

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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.”
Ground state solutions for the nonlinear Schrödinger–Maxwell equations (2007, unknown): “The nonlinear case has been considered in [1, 10, 13, 15, 20], where existence and multiplicity results have been stated when V is a positive constant.”
Non-Existence Results for the Coupled Klein-Gordon-Maxwell Equations (2004, background): “6) with f(u) = |u|p−2u, the existence of a nontrivial radial solution was proved in [7] under the restriction 4 < p < 6 and in [10] for 4 ≤ p < 6, while in [12] the existence of a non-radially symmetric solution was established for 2 < p < 6.”
Sign-changing radial solutions for the Schr\"odinger-Poisson-Slater problem (2011, background): “1) shows several difficulties, the nonlinear nature of it being due both to the power-type nonlinearity in the first equation and to the coupling, and has been object of many investigation in the last years (we recall among others the papers [1], [2], [4], [9]–[12], [16], [19]–[21], [26], see also [”