  In this paper we discuss an extension of some results obtained by E. Serra
and P. Tilli, in [Serra&Tilli '12, Serra&Tilli '16], concerning an original
conjecture by E. De Giorgi ([De Giorgi '96, De Giorgi '06]) on a purely
minimization approach to the Cauchy problem for the defocusing nonlinear wave
equation. Precisely, we show how to extend the techniques developed by Serra
and Tilli for homogeneous hyperbolic nonlinear PDEs to the nonhomogeneous case,
thus proving that the idea of De Giorgi yields in fact an effective approach to
investigate general hyperbolic equations.
