Abstract
In this paper, we study the existence and multiplicity results for the nonlinear Schrödinger–Poisson systems (∗) { − Δ u + V ( x ) u + K ( x ) ϕ ( x ) u = f ( x , u ) , in R 3 , − Δ ϕ = K ( x ) u 2 , in R 3 . Under certain assumptions on V , K and f , we obtain at least one nontrivial solution for ( ∗ ) without assuming the Ambrosetti and Rabinowitz condition by using the mountain pass theorem, and obtain infinitely many high energy solutions when f ( x , ⋅ ) is odd by using the fountain theorem.
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