Some properties of the Dulac functions set

Abstract

In order to rule out the existence of periodic orbits in the plane for a given system of differential equations, we discuss the feature of the set of Dulac functions, establishing some of its properties as well as some results for special cases where this set of functions is not empty. We give some examples to illustrate applications of these results.

Keywords

• bendixson-dulac criterion
• dulac functions
• periodic orbits