Abstract

We prove that any classical Liénard equation of degree four has at most one limit cycle, and the limit cycle is hyperbolic if it exists. This result gives a positive answer to the conjecture by A. Lins, W. de Melo and C.C. Pugh in 1977 about the number of limit cycles for polynomial Liénard equations for n=4.

In the talk I will first introduce the background of the problem, then talk about how to transform the equations to a good form, and how to study the divergence integral in different cases, in order to prove the main result.

This is a recent work with Jaume Llibre.