Electron. J. Diff. Equ., Vol. 2012 (2012), No. 22, pp. 1-17.

Limit cycles for fourth-order autonomous differential equations

Jaume Llibre, Amar Makhlouf

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 7, 2012.
Math Subject Classifications: 37G15, 37C80, 37C30.
Key Words: Periodic orbit; fourth-order differential equation; averaging theory.

Show me the PDF file (275 KB), TEX file, and other files for this article.

Jaume Llibre
Departament de Matematiques
Universitat Autonoma de Barcelona
08193 Bellaterra, Barcelona, Catalonia, Spain
email: jllibre@mat.uab.cat
Amar Makhlouf
Department of Mathematics, University of Annaba
BP 12, Annaba, Algeria
email: makhloufamar@yahoo.fr

Return to the EJDE web page