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.