Research Article
Existence and concentration of solutions for nonlinear Schrödinger-Poisson system with steep potential well
https://doi.org/10.21203/rs.3.rs-3141933/v1
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In this paper, we consider the existence and concentration of solutions of the Schrödinger-Poisson system −∆u + λV(x)u + K(x)φu = f (x, u), in R 3 , −∆φ = K(x)u 2 , in R 3 , where λ > 0 is a parameter. Under some suitable assumptions on V, K, and f , the existence and concentration of solutions are obtained by using variational methods.
2020 Mathematics Subject Classification: 35A15, 35B38, 35D30
Schrodinger-Poisson system
Variational methods
(PS )c condition
concentration
steep potential well
No competing interests reported.
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