Existence and concentration of solutions of Schrödinger-Poisson system

Abstract The aim of this paper is to study the following Schrodinger–Poisson problem ( SP ) − △ u + V ( x ) u + e ϕ ( x ) u = λ f ( u ) , in R 3 , − △ ϕ = u 2 , lim | x | → + ∞ ϕ ( x ) = 0 , in R 3 , u > 0 , in R 3 . We prove existence and concentration of positive solutions to system ( SP ) for suitable range of e and λ .

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