Uniqueness of Limit Cycle For Liénard differential Equations of Degree Four
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 [4] in 1977 about the number of limit cycles for polynomia...
| Authors: | ; |
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| Format: | Article |
| Publication date: | 2012 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:150546 |
| Online Access: | https://ddd.uab.cat/record/150546 https://dx.doi.org/urn:doi:10.1016/j.jde.2011.11.002 |
| Access Level: | Open access |
| Keyword: | Liénard equations Limit cycle |
| Summary: | 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 [4] in 1977 about the number of limit cycles for polynomial Liénard differential equations for n = 4. |
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