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Existence of infinitely many large solutions for the nonlinear Schrödinger-Maxwell equations. (English) Zbl 1189.35081

Summary: We study the nonlinear stationary Schrödinger-Maxwell equations

-Δu+V(x)u+φu=f(x,u)in 3 ,-Δφ=u 2 in 3 ·(*)

Using the variant fountain theorem introduced by W. Zou [Manuscr. Math. 104, No. 3, 343–358 (2001; Zbl 0976.35026)], under certain assumptions on V and f, we get infinitely many large solutions for (*).

35J47Second-order elliptic systems
35J50Systems of elliptic equations, variational methods
35Q40PDEs in connection with quantum mechanics
35B40Asymptotic behavior of solutions of PDE