Geodesic
Limit cycles for fourth-order autonomous differential equations
Electronic journal of differential equations, Tome 2012 (2012)
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},
     year = {2012},
     volume = {2012},
     zbl = {1243.37044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a30/}
}
TY  - JOUR
AU  - Llibre,  Jaume
AU  - Makhlouf,  Amar
TI  - Limit cycles for fourth-order autonomous differential equations
JO  - Electronic journal of differential equations
PY  - 2012
VL  - 2012
UR  - http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a30/
LA  - en
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ER  - 
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%A Llibre,  Jaume
%A Makhlouf,  Amar
%T Limit cycles for fourth-order autonomous differential equations
%J Electronic journal of differential equations
%D 2012
%V 2012
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a30/
%G en
%F EJDE_2012__2012__a30
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/