Multiplicity of normalized solutions for a class of nonlinear Schr?dinger-Poisson-Slater equations

摘要

In this paper, we prove a multiplicity result of solutions for the following stationary Schr?dinger-Poisson-Slater equations -?u - λu + (|x|~(-1) * |u|~2)u - |u|~(|-2)u = 0 in R~3, (0.1) where λ ∈ R is an undetermined parameter, and p ∈ (10/3,6). We obtain couple solutions (u, λ) with u having a prescribed L2-norm. Our proofs are mainly inspired by a recent work of Bartsch and De Valeriola [7].