  We show the existence of homoclinic type solutions of second order
Hamiltonian systems with a potential satisfying a relaxed superquadratic growth
condition and a forcing term that is sufficiently small in the space of square
integrable functions. The idea of our proof is to approximate the original
system by time-periodic ones, with larger and larger time-periods. We prove
that the latter systems admit periodic solutions of mountain-pass type, and
obtain homoclinic type solutions of the original system from them by passing to
the limit (in the topology of almost uniform convergence) when the periods go
to infinity.
