Multiple solutions for superlinear Schrödinger-Poisson system with sign-changing potential and nonlinearity

In this paper, we study the following Schrodinger-Poisson system { - Δ u + V ( x ) u + λ ? ( x ) u = f ( x , u ) , in? R 3 , - Δ ? = u 2 , in? R 3 , where the nonlinearity f and the potential V are allowed to be sign-changing. Under some appropriate assumptions on V and f , we obtain the existence of two different solutions of the system via the Ekeland's variational principle and the Mountain Pass Theorem.

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