Positive solutions for Schrödinger–Poisson equations with a critical exponent

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Existence and multiplicity of solutions for Schrödinger–Poisson equations with sign-changing potential (2015, background): “There has been a vast literature on the study of existence and multiplicity of solutions of system (SP )λ under various hypotheses on the potential V (x) and the nonlinearity f(x, u), see [1-3, 5, 9-14, 18, 19, 21, 22, 24-28, 31, 34, 35-37] and the references therein.”
Existence of least energy nodal solution for a Schrödinger–Poisson system in bounded domains (2013, methodology): “case where Ω = R , see the papers of Azzollini & Pomponio [5], Cerami & Vaira [13], Coclite [14], D’Aprile & Mugnai [15, 16], d’Avenia [17], Ianni [20], Kikuchi [19], and Zhao & Zhao [29].”
Existence and concentration of positive ground states for a Kirchhoff equation involving critical Sobolev exponent (2014, methodology): “It is not hard to verify (iii) and (iv); See, for example, Zhao and Zhao [47].”
Ground State Solutions for the Nonlinear Schrödinger–Bopp–Podolsky System with Critical Sobolev Exponent (2020, methodology): “Motivated by [1, 10, 20, 26], we choose the usual Sobolev spaceH1(R3) to prove the existence of ground state solutions for the “limit” problem”