The bifurcation of limit cycles in the system
is studied for small . It is assumed that is a real polynomial of degree or and are natural numbers. The main result states that an upper bound for the number of limit cycles bifurcating from the periodic orbits of the initial system () is given by where
Moreover, there are systems with at least limit cycles.
The proof follows from an estimation of the number of positive zeros of the integral which is elementary and is calculated explicitly in the paper.
(Reviewer’s remark). The integral , as taken by the authors, is identically zero. One should consider a similar integral with instead of in order to obtain information about the limit cycles in the perturbed system.