Existence and concentration of solutions for the Schrödinger-Poisson equations with steep well potential

Abstract In this paper we study a system of Schrodinger–Poisson equations { − Δ u + λ V ( x ) u + K ( x ) ϕ u = | u | p − 2 u , in R 3 , − Δ ϕ = K ( x ) u 2 , in R 3 , where λ > 0 is a parameter, 2 p 6 . Under suitable assumptions on V and K, the existence of nontrivial solution and concentration results are obtained via variational methods. In particular, the potential V is allowed to be sign-changing for the case p ∈ ( 4 , 6 ) .

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