A New Criterion for Controlling the Number of Limit Cycles of Some Generalized Liénard Equations

✍ Scribed by Armengol Gasull; Hector Giacomini

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 180 KB
• Volume: 185
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.2002.4172

✦ Synopsis

We consider a class of planar differential equations which include the Lie´nard differential equations. By applying the Bendixson-Dulac Criterion for '-connected sets we reduce the study of the number of limit cycles for such equations to the condition that a certain function of just one variable does not change sign. As an application, this method is used to give a sharp upper bound for the number of limit cycles of some Lie´nard differential equations. In particular, we present a polynomial Lie´nard system with exactly three limit cycles.