THE ROLE OF THE SCALAR CURVATURE IN SOME SINGULARLY PERTURBED COUPLED ELLIPTIC SYSTEMS ON RIEMANNIAN MANIFOLDS

Given a 3-dimensional Riemannian manifold (M, g), we investigate the existence of positive solutions of the Klein-Gordon-Maxwell system [GRAPHICS] and Schrodinger-Maxwell system [GRAPHICS] when p is an element of (2, 6). We prove that if epsilon is small enough, any stable critical point xi(0) of the scalar curvature of g generates a positive solution (u(epsilon), v(epsilon)) to both the systems such that u(epsilon) concentrates at xi(0) as epsilon goes to zero