Limit cycles of a class of generalized Liénard polynomial equations

Abstract

We prove that the generalized Liénard polynomial differential system x'=y^2p-1, y'=-x^2q-1 - f(x) y^2n-1, where p, q, and n are positive integers; is a small parameter; and f(x) is a polynomial of degree m which can have [m/2] limit cycles, where [x] is the integer part function of x.