Schrodinger-Maxwell systems on compact Riemannian manifolds

In this paper, we are focusing to the following Schrodinger-Maxwell system: {-Delta(g)u + beta(x)u + eu phi = Psi(lambda,x)f(u) in M, (SM Psi(lambda,.)e) -Delta(g)phi + phi = qu(2) in M, where (M, g) is a 3-dimensional compact Riemannian manifold without boundary, e, q > 0 are positive numbers, f : R -> R is a continuous function, beta is an element of C-infinity(M) and Psi is an element of C-infinity(R+ x M) are positive functions. By various variational approaches, existence of multiple solutions of the problem (SM Psi(lambda,.)e) is established.