Number and profile of low energy solutions for singularly perturbed Klein-Gordon-Maxwell systems on a Riemannian manifold

Given a 3-dimensional Riemannian manifold (M,g), we investigate the existence of positive solutions of the Klein-Gordon-Maxwell system{−ε2Δgu+au=up−1+ω2(qv−1)2uin M,−Δgv+(1+q2u2)v=qu2in M and Schrödinger-Maxwell system{−ε2Δgu+u+ωuv=up−1in M,−Δgv+v=qu2in M when p∈(4,6). We prove that the number of one peak solutions depends on the topological properties of the manifold M, by means of the Lusternik Schnirelmann category.