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Azzollini, A.; Pomponio, A.
Journal of mathematical analysis and applications, 09/2008, Letnik: 345, Številka: 1Journal Article
In this paper we study the nonlinear Schrödinger–Maxwell equations { − Δ u + V ( x ) u + ϕ u = | u | p − 1 u in R 3 , − Δ ϕ = u 2 in R 3 . If V is a positive constant, we prove the existence of a ground state solution ( u , ϕ ) for 2 < p < 5 . The non-constant potential case is treated for 3 < p < 5 , and V possibly unbounded below. Existence and nonexistence results are proved also when the nonlinearity exhibits a critical growth.
