Existence of infinitely many large solutions for the nonlinear Schrödinger–Maxwell equations

Abstract In this paper, we study the nonlinear stationary Schrodinger–Maxwell equations (∗) { − Δ u + V ( x ) u + ϕ u = f ( x , u ) , in  R 3 , − Δ ϕ = u 2 , in  R 3 . Using the variant fountain theorem introduced by Zou [W. Zou, Variant fountain theorems and their applications, Manuscripta Math. 104 (2001) 343–358], under certain assumptions on V and f , we get infinitely many large solutions for (∗) .

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