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We show the existence of homoclinic type solutions of second orderHamiltonian systems with a potential satisfying a relaxed superquadratic growthcondition and a forcing term that is sufficiently small in the space of squareintegrable functions. The idea of our proof is to approximate the originalsystem by time-periodic ones, with larger and larger time-periods. We provethat the latter systems admit periodic solutions of mountain-pass type, andobtain homoclinic type solutions of the original system from them by passing tothe limit (in the topology of almost uniform convergence) when the periods goto infinity.

On the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems