We prove that any classical Liénard differential 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 (1977)  about the number of limit cycles for polynomial Liénard differential equations for n = 4. © 2011 Elsevier Inc.
- Limit cycle
- Liénard equations