Multiplicity of normalized solutions for a class of nonlinear Schrödinger–Poisson–Slater equations

In this paper, we prove a multiplicity result of solutions for the following stationary Schrödinger–Poisson–Slater equations(0.1) − Δ u − λ u + ( | x | − 1 ⁎ | u | 2 ) u − | u | p − 2 u = 0 in R 3 , where λ ∈ R is an undetermined parameter, and p ∈ ( 10 3 , 6 ) . We obtain couple solutions ( u , λ ) with u having a prescribed L 2 -norm. Our proofs are mainly inspired by a recent work of Bartsch and De Valeriola [7].