Geodesic
Limit cycles for fourth-order autonomous differential equations
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We provide sufficient conditions for the existence of periodic solutions of the fourth-order differential equation $$ \ddddot x -(\lambda+\mu) \dddot x +(1+\lambda \mu)\ddot x -(\lambda+\mu)\dot x+\lambda \mu x = \varepsilon F(x, \dot x, \ddot x, \dddot x), $$ where $\lambda, \mu$ and $\varepsilon$ are real parameters, $\varepsilon$ is small and F is a nonlinear function.
Classification : 37G15, 37C80, 37C30
Keywords: periodic orbit, fourth-order differential equation, averaging theory 
@article{EJDE_2012__2012__a30,
     author = {Llibre, Jaume and Makhlouf, Amar},
     title = {Limit cycles for fourth-order autonomous differential equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a30/}
}
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Llibre, Jaume; Makhlouf, Amar. Limit cycles for fourth-order autonomous differential equations. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a30/