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

Stability, Resonance and Lyapunov Inequalities for Periodic Conservative Systems