Periodic orbits of a non-autonomous quadratic differential system obtained from third-order differential equations

Abstract

We provide sufficient conditions for the existence of periodic solutions of the third-order differential equations

where a ₀, a ₁, b ₀, b ₁, c ₂ are real arbitrary parameters with b ₀ > 0, ϵ is a small parameter and F is a -periodic nonlinear function in the variable t. The prime denotes derivative with respect to the independent variable t. Moreover we provide an application.

Keywords:

• periodic orbit
• third-order differential equation
• quadratic system
• averaging theory

AMS Subject Classifications:

• 37G15
• 37C80
• 37C30

Acknowledgements

The first author is partially supported by a MICIIN/FEDER grant MTM2008–03437, by a CIRIT grant number 2009SGR–410 and by ICREA Academia.