Wednesday, February 20, 2013

1302.4734 (Marco Ghimenti et al.)

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

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.
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