  Under the validity of a Landesman-Lazer type condition, we prove the
existence of solutions bounded on the real line, together with their first
derivatives, for some second order nonlinear differential equation of the form
$\ddot u + g(u) = p(t)$, where the reaction term $g$ is bounded. The proof is
variational, and relies on a dual version of the Nehari method for the
existence of oscillating solutions to superlinear equations.
