On the Schrodinger-Poisson system with indefinite potential and 3-sublinear nonlinearity

We consider a class of stationary Schrodinger-Poisson systems with a general nonlinearity f(u) and coercive sign-changing potential V so that the Schrodinger operator -Delta + V is indefinite. Previous results in this framework required f to be strictly 3-superlinear, thus missing the paramount case of the Gross-Pitaevskii-Poisson system, where f(t) = vertical bar t vertical bar(2)t; in this paper we fill this gap, obtaining non-trivial solutions when fis not necessarily 3-superlinear. (C) 2020 Elsevier Inc. All rights reserved.