  This paper is devoted to the study of Lyapunov type inequalities for periodic
conservative systems. The main results are derived from a previous analysis
which relates the best Lyapunov constants to some especial (constrained or
unconstrained) minimization problems. We provide some new results on the
existence and uniqueness of solutions of nonlinear resonant and periodic
systems. Finally, we present some new conditions which guarantee the stable
boundedness of linear periodic conservative systems.
