On the uniqueness of limit cycles for Li\'enard equation: the legacy of G. Sansone

TL;DR

This paper reviews the history of limit cycle uniqueness in Lie9nard equations, culminating in a new theorem that extends previous geometric methods to establish uniqueness.

Contribution

It introduces a novel uniqueness theorem for limit cycles in Lie9nard equations, building on Sansone-Massera's geometric approach.

Findings

Comprehensive review of existing results on limit cycle uniqueness

Introduction of a new geometric uniqueness theorem

Extension of Sansone-Massera's approach to broader cases

Abstract

We give an account of the results about limit cycle's uniqueness for Li\'enard equations, from Levinson-Smith's one to the most recent ones. We present a new uniqueness theorem in the line of Sansone-Massera's geometrical approach.