Positive and sign-changing solutions of a Schrödinger–Poisson system involving a critical nonlinearity

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Existence and concentration of positive ground states for a Kirchhoff equation involving critical Sobolev exponent (2014, unknown): “[23], we know that ∫ (Q(x∗) − Q( x))|Uε|(6) ≤ C1ε (1)2 .”
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.”