Limit Cycles of a Class of Generalized Liénard Polynomial Equations

Abstract

We prove that the generalized Liénard polynomial differential system $$ \dot x = y^{2p-1}, \qquad \dot y= -x^{2q-1}-\varepsilon f(x)\, y^{2n-1}, $$ (1) where p, q, and n are positive integers; ε 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.