On the construction of Dulac-Cherkas functions for generalized Liénard systems

Abstract

Dulac-Cherkas functions can be used to derive an upper bound for the number of limit cycles of planar autonomous differential systems, at the same time they provide information about their stability. In this paper we present a method to construct such functions for generalized Liénard systems by means of linear differential equations. If the degree m of the polynomial is not greater than 3, then the described algorithm works generically. By means of an example we show that this approach can be applied also to polynomials with degree m larger than 3.