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

Abstract 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 − Δ + 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 ) = | t | 2 t ; in this paper we fill this gap, obtaining non-trivial solutions when f is not necessarily 3-superlinear.