The multiplicity of homoclinic solutions is obtained for a class of the p-Laplacian Hamiltonian systems d d t (| u ˙ (t) | p − 2 u ˙ (t)) − a (t) | u (t) | p − 2 u (t) + ∇ W (t , u (t)) = 0 via variational methods, where a (t) is neither coercive nor bounded necessarily and W (t , u) is under new concave–convex conditions. Recent results in the literature are generalized even for p = 2 .