Solutions for a class of Schrödinger–Poisson system in bounded domains

In this paper, we apply the methods of Nehari manifold to study a class of Schrödinger–Poisson system in a bounded domain Ω ⊂ R 3 submitted to Dirichlet boundary conditions. Under a general 4-superlinear conditions on the nonlinearity f , we prove the existence of a ground state solution. In case the nonlinearity f is odd with respect to the second variable, we obtain the existence of infinitely many solutions. In the proofs, the Nehari manifold does not need to be of C 1 class.