  Roughly speaking a solitary wave is a solution of a field equation whose
energy travels as a localized packet and which preserves this localization in
time. A solitary wave which has a non-vanishing angular momentum is called
vortex.
  We know (at least) three mechanisms which might produce solitary waves and
vortices:
  1) Complete integrability, (e.g. Kortewg-de Vries equation)
  2) Topological constraints, (e.g. Sine-Gordon equation);
  3) Ratio energy/charge: (e.g. the nonlinear Klein-Gordon equation).
  The third type of solitary waves or solitons will be called hylomorphic. This
class includes the Q-balls which are spherically symmetric solutions of the
nonlinear Klein-Gordon equation (NKG) as well as solitary waves and vortices
which occur, by the same mechanism, in the nonlinear Schroedinger equation and
in gauge theories.
  This paper is devoted to an abstract theorem which allows to prove the
existence of hylomorphic solitary waves, solitons and vortices in the (NKG) and
in the nonlinear Klein-Gordon-Maxwell equations (NKGM)
