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February  2010, 27(1): 217-229. doi: 10.3934/dcds.2010.27.217

Upper bounds for the number of limit cycles of some planar polynomial differential systems

Armengol Gasull 1, and  Hector Giacomini 2,

1. 

Dept. de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193 Bellaterra, Barcelona
2. 

Laboratoire de Mathématique et Physique Théorique, C.N.R.S. UMR 7350, Faculté des Sciences et Techniques, Université de Tours, Parc de Grandmont,37200 Tours, France

Received  July 2009 Revised  November 2009 Published  February 2010

We give an effective method for controlling the maximum number of limit cycles of some planar polynomial systems. It is based on a suitable choice of a Dulac function and the application of the well-known Bendixson-Dulac Criterion for multiple connected regions. The key point is a new approach to control the sign of the functions involved in the criterion. The method is applied to several examples.
Keywords: Dulac function., limit cycle, Polynomial differential system.
Mathematics Subject Classification: Primary: 34C05, 34C07; Secondary: 37C2.
Citation: Armengol Gasull, Hector Giacomini. Upper bounds for the number of limit cycles of some planar polynomial differential systems. Discrete & Continuous Dynamical Systems, 2010, 27 (1) : 217-229. doi: 10.3934/dcds.2010.27.217
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