×

Some properties of the Dulac functions set. (English) Zbl 1340.34121

Summary: 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.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI