Normalized solutions for Schrodinger-Poisson equations with general nonlinearities

In this paper, we prove the existence of normalized solutions to the following Schrodinger-Poisson equation -Delta u + (vertical bar x vertical bar(-1) * vertical bar u vertical bar(2))u - f(u) = lambda u, x is an element of R-3, lambda is an element of R, where f is an element of C(R, l) satisfies more general conditions which cover the case f(u) similar to lulg-2u with q is an element of (3, 3) U (10/3, 6). Especially, some new analytical techniques are presented to overcome the difficulties due to the presence of three terms in the corresponding energy functional which scale differently. (C) 2019 Elsevier Inc. All rights reserved.