Abstract
In this paper, we study the following Schrödinger–Poisson system {−Δu+V(x)u+λϕ(x)u=f(x,u),in R3,−Δϕ=u2,in R3, 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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