We consider the system Ju ̇ =∇H(u)+f(u)+p(t), where H : R^2 → R is of class C^1 with locally Lipschitz continuous gradient, f : R^2 → R^2 is locally Lipschitz continuous and bounded, and p : R → R^2 is measurable, bounded and T −periodic. Here, J is the standard symplectic matrix. For some classes of functions f, we give new existence theorems for periodic solutions and for unbounded solutions. Applications are given to forced second-order differential equations with separated nonlinearities.
