Stability, Resonance and Lyapunov Inequalities for Periodic Conservative Systems

TL;DR

This paper investigates Lyapunov inequalities for periodic conservative systems, establishing new conditions for stability, existence, and uniqueness of solutions, and linking Lyapunov constants to minimization problems.

Contribution

It introduces novel Lyapunov inequalities and stability criteria for nonlinear and linear periodic conservative systems, expanding theoretical understanding.

Findings

New Lyapunov inequalities for periodic systems

Conditions ensuring stable boundedness of solutions

Existence and uniqueness results for nonlinear resonant systems

Abstract

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.