Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 22, pp. 1-17.

Title: Limit cycles for fourth-order autonomous differential equations

Authors: Jaume Llibre  (Univ. Autonoma de Barcelona, Spain)
         Amar Makhlouf (University of Annaba,  Algeria)

Abstract:
 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.

Submitted October 12, 2011. Published February 07, 2012.
Math Subject Classifications: 37G15, 37C80, 37C30.
Key Words: Periodic orbit; fourth-order differential equation;
           averaging theory.