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In this paper, we are concerned with the following SchrödingerPoisson-Slater problem with critical growth: −∆u+ (u ? 1 |4πx| )u = μk(x)|u| u+ |u|u in R. We use a measure representation concentration-compactness principle of Lions to prove that the (PS)c condition holds locally. Via a truncation technique and Krasnoselskii genus theory, we further obtain infinitely many solutions for μ ∈ (0, μ∗) with some μ∗ > 0.

INFINITELY MANY SOLUTIONS FOR A ZERO MASS SCHRÖDINGER-POISSON-SLATER PROBLEM WITH CRITICAL GROWTH