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

الأصل · EN

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 x₀ of the scalar curvature of the manifold (M,g) generates a positive solution (uₑps,vₑps) to both the systems such that uₑps concentrates at xi₀ as epsilon goes to zero.