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 equationsequation(0.1)−Δu−λu+(|x|−1⁎|u|2)u−|u|p−2u=0in R3, where λ∈Rλ∈R is an undetermined parameter, and p∈(103,6). We obtain couple solutions (u,λ)(u,λ) with u   having a prescribed L2L2-norm. Our proofs are mainly inspired by a recent work of Bartsch and De Valeriola [7].