Nonlinear Klein-Gordon-Maxwell systems with Neumann boundary conditions   on a Riemannian manifold with boundary
  Let (M,g) be a smooth compact, n dimensional Riemannian manifold, n=3,4 with smooth n-1 dimensional boundary. We search the positive solutions of the singularly perturbed Klein Gordon Maxwell Proca system with homogeneous Neumann boundary conditions or for the singularly perturbed Klein Gordon Maxwell system with mixed Dirichlet Neumann homogeneous boundary conditions. We prove that stable critical points of the mean curvature of the boundary generates solutions when the perturbation parameter is sufficiently small. 
Marco Ghimenti and Anna Maria Micheletti
math.AP math-ph math.MP