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Periodic solutions of the Rayleigh equation with damping of definite sign

Pierpaolo OmariGabriele Villari — 1990

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The existence of a non-trivial periodic solution for the autonomous Rayleigh equation x ¨ + F x ˙ + g x = 0 is proved, assuming conditions which do not imply that F x x has a definite sign for x large. A similar result is obtained for the periodically forced equation x ¨ + F x ˙ + g x = e t .

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