Some multiplicity results of homoclinic solutions for second order Hamiltonian systems

We look for homoclinic solutions q : R ! RN to the class of second order Hamiltonian systems - q'' + L(t)q = a(t)rG1(q) - b(t)rG2(q) + f(t), t 2 R, where L : R ! R^NXN and a; b : R ! R are positive bounded functions, G1;G2 : RN ! R are positive homogeneous functions and f : R ! RN. Using variational techniques and the Pohozaev fibering method, we prove the existence of infinitely many solutions if f = 0 and the existence of at least three solutions if f is not trivial but small enough.