We deal with the following second-order Hamiltonian systems u - L(t)u + del W (t, u) = 0, where L is an element of C(R,R-N2) is a symmetric and positive define matrix for all t is an element of R, W is an element of C-1 (R x R-N, R) and del W(t, u) is the gradient of W with respect to u. Under the superquadratic condition, we obtain the existence of ground state homoclinic orbits by means of the generalized Nehari manifold developed by Szulkin and Weth. Under the subquadratic condition, we employ variational techniques and the concentration-compactness principle to establish new criteria guara...
