Multiplicity of normalized solutions for a class of nonlinear Schrodinger-Poisson-Slater equations

In this paper, we prove a multiplicity result of solutions for the following stationary Schrodinger-Poisson-Slater equations -Delta u - lambda u + (vertical bar x vertical bar(-1) * vertical bar u vertical bar(2))u - vertical bar u vertical bar(p-2)u = 0 in R-3, (0.1) where lambda is an element of R is an undetermined parameter, and p is an element of (10/3, 6). We obtain couple solutions (u, lambda) with u having a prescribed L-2-norm. Our proofs are mainly inspired by a recent work of Bartsch and De Valeriola [7]. (C) 2014 Elsevier Inc. All rights reserved.