Abstract

In this work we prove a criterion for the existence, uniqueness and to bound the number of limit cycles, for some family of generalized Liénard equation $x\prime =y2n+1$, $y\prime =-g(x)-f(x)y2k+1$. Next we apply our result to bound the number of limit cycles for a Kukles family of differential equations. The proof of this criterion is partially based on a generalization of some geometrical ideas used in former known results on the Liénard equation.

This is a joint work with Bartomeu Coll and Faust Mas.