Stability, Resonance and Lyapunov Inequalities for Periodic Conservative Systems

2010/09/15 by A. Cañada, Antonio Canada, Canada, Antonio +2
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #Control and Stability of Dynamical Systems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Quantum chaos and dynamical systems #math.CA

paper · pdf · doi:10.48550/arxiv.1009.2882

19 pages

arxiv created 2010/09/15 · openalex publication_date 2010/09/15 · arxiv updated 2010/09/16 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

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.

Citations

• Matrix Lyapunov inequalities for ordinary and elliptic partial differential equations

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