Periodic solutions of the Rayleigh equation with damping of definite sign

Pierpaolo Omari; Gabriele Villari

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1990)

  • Volume: 1, Issue: 1, page 29-35
  • ISSN: 1120-6330

Abstract

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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 .

How to cite

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Omari, Pierpaolo, and Villari, Gabriele. "Periodic solutions of the Rayleigh equation with damping of definite sign." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 1.1 (1990): 29-35. <http://eudml.org/doc/244117>.

@article{Omari1990,
abstract = {The existence of a non-trivial periodic solution for the autonomous Rayleigh equation \( \ddot\{x\} + F(\dot\{x\}) + g(x) = 0 \) 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 \( \ddot\{x\} + F(\dot\{x\}) + g(x) = e(t) \).},
author = {Omari, Pierpaolo, Villari, Gabriele},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Periodic solutions; Nonlinear ordinary differential equations; Limit-cycles; limit cycles; autonomous Rayleigh equation},
language = {eng},
month = {2},
number = {1},
pages = {29-35},
publisher = {Accademia Nazionale dei Lincei},
title = {Periodic solutions of the Rayleigh equation with damping of definite sign},
url = {http://eudml.org/doc/244117},
volume = {1},
year = {1990},
}

TY - JOUR
AU - Omari, Pierpaolo
AU - Villari, Gabriele
TI - Periodic solutions of the Rayleigh equation with damping of definite sign
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1990/2//
PB - Accademia Nazionale dei Lincei
VL - 1
IS - 1
SP - 29
EP - 35
AB - The existence of a non-trivial periodic solution for the autonomous Rayleigh equation \( \ddot{x} + F(\dot{x}) + g(x) = 0 \) 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 \( \ddot{x} + F(\dot{x}) + g(x) = e(t) \).
LA - eng
KW - Periodic solutions; Nonlinear ordinary differential equations; Limit-cycles; limit cycles; autonomous Rayleigh equation
UR - http://eudml.org/doc/244117
ER -

References

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