Schrödinger-Maxwell systems on non-compact Riemannian manifolds

In this paper we study nonlinear Schr¨odinger–Maxwell systems on n-dimensional non-compact Riemannian manifolds of Hadamard type, 3 ≤ n ≤ 5. The main difficulty resides in the lack of compactness which is recovered by exploring suitable isometric actions of the Hadamard manifolds. By combining variational arguments, some existence, uniqueness and multiplicity of isometry-invariant weak solutions are established for the Schr¨odinger–Maxwell system depending on the behavior of the nonlinear term