A note on bounded, periodic and stable solutions of differential equations
J. Knežević-Miljanović (1987)
Matematički Vesnik
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J. Knežević-Miljanović (1987)
Matematički Vesnik
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Hale, Jack K.
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M. Sabatini (1993)
Rendiconti del Seminario Matematico della Università di Padova
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Jiří Šremr (2025)
Applications of Mathematics
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We discuss Lyapunov stability/instability of both lower and upper equilibria of free damped pendulum with periodically oscillating suspension point. We recall the results of Bogolyubov and Kapitza, provide new effective criteria of stability/instability of the equilibria of pendulum equation, and give the exact and complete proofs. The criteria obtained are formulated in terms of positivity/negativity of Green's functions of the periodic boundary value problems for linearized equations....
L. Erbe (1975)
Annales Polonici Mathematici
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Lian, Jin-Guo (2009)
Applied Mathematics E-Notes [electronic only]
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Patrizio Colaneri (2000)
Kybernetika
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The paper is divided in two parts. In the first part a deep investigation is made on some system theoretical aspects of periodic systems and control, including the notions of and norms, the parametrization of stabilizing controllers, and the existence of periodic solutions to Riccati differential equations and/or inequalities. All these aspects are useful in the second part, where some parametrization and control problems in and are introduced and solved.