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| Given a 3 or a 4 dimensional Riemannian manifold $(M;g)$, we investigate the
existence of positive solutions of a singularly perturbed Klein-Gordon-Maxwell
system in $M$.
When the nonlinearity is subcritical, both the topology and the geometry of
the Riemannian manifold $M$ influence the number of solution. In the case of
critical or supercritical nonlinearity, if the manifold $M$ exhibits some special type
of symmetry, it is possible to find solutions of the KGM equation concentrating
on a submanifold of $M.$ |
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