Abstract
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) [4] about the number of limit cycles for polynomial Liénard differential equations for n = 4. © 2011 Elsevier Inc.
Original language | English |
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Pages (from-to) | 3142-3162 |
Journal | Journal of Differential Equations |
Volume | 252 |
Issue number | 4 |
DOIs | |
Publication status | Published - 15 Feb 2012 |
Keywords
- Limit cycle
- Liénard equations