This paper is devoted to the study of solitons whose existence is related to
the ratio energy/charge. These solitons are called hylomorphic. In the first
part of the paper we prove an abstract theorem on the existence of
hylomorphic solitons which can be applied to the main situations considered
in literature. In the second part, we apply this theorem to the nonlinear
Schrödinger and Klein Gordon equations defined on a lattice.