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Let (M,g) be a smooth compact, n dimensional Riemannian manifold, n=3,4 withsmooth n-1 dimensional boundary. We search the positive solutions of thesingularly perturbed Klein Gordon Maxwell Proca system with homogeneous Neumannboundary conditions or for the singularly perturbed Klein Gordon Maxwell systemwith mixed Dirichlet Neumann homogeneous boundary conditions. We prove thatstable critical points of the mean curvature of the boundary generatessolutions when the perturbation parameter is sufficiently small.

Nonlinear Klein-Gordon-Maxwell systems with Neumann boundary conditions on a Riemannian manifold with boundary