Abstract In this paper, we study the following quasilinear Schrödinger equation: $$ -\operatorname{div}\bigl(a(x,\nabla u)\bigr)+V(x) \vert x ^{-\alpha p^{*}} u ^{p-2}u=K(x) ^{- \alpha p^{*}}f(x,u) \quad \text{in } \mathbb{R}^{N}, − div ( a x ...

In this article we study the existence of infinitely many large energy solutions for the superlinear Schrödinger-Maxwell equations −∆u+ V (x)u+ φu = f(x, u) in R, −∆φ = u, in R, via the Fountain Theorem in critical point theory. In particular, we do not use the classical Ambrosetti-Rabinowitz condition.

where V : R → R and f : R × R → R. In the past several decades, the existence and multiplicity of nontrivial solutions for problem (1.1) have been extensively investigated in the literature with the aid of critical point theory and variational methods. Many papers deal with the autonomous case where the potential V and the nonlinearity f are independent of x, or with the radially symmetric case...