1302.4734 (Marco Ghimenti et al.)

The role of the scalar curvature in some singularly perturbed coupled
elliptic systems on Riemannian manifolds    [PDF]

Marco Ghimenti, Anna Maria Micheletti, Angela Pistoia

Given a 3-dimensional Riemannian manifold (M,g), we investigate the existence of positive solutions of singularly perturbed Klein-Gordon-Maxwell systems and Schroedinger-Maxwell systems on M, with a subcritical nonlinearity. We prove that when the perturbation parameter epsilon is small enough, any stable critical point x_0 of the scalar curvature of the manifold (M,g) generates a positive solution (u_eps,v_eps) to both the systems such that u_eps concentrates at xi_0 as epsilon goes to zero.

View original: http://arxiv.org/abs/1302.4734