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Some Applications of the Extended Bendixson-Dulac Theorem

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Progress and Challenges in Dynamical Systems

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 54))

Abstract

During the last years the authors have studied the number of limit cycles of several families of planar vector fields. The common tool has been the use of an extended version of the celebrated Bendixson-Dulac Theorem. The aim of this work is to present an unified approach of some of these results, together with their corresponding proofs. We also provide several applications.

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Acknowledgements

First author is supported by the MICIIN/FEDER grant number MTM2008-03437 and the Generalitat de Catalunya grant number 2009SGR410.

Author information

Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193, Bellaterra, Barcelona, Spain

    Armengol Gasull

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

    Hector Giacomini

Authors
  1. Armengol Gasull
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  2. Hector Giacomini
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Corresponding author

Correspondence to Armengol Gasull .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Oviedo, Oviedo, Spain

    Santiago Ibáñez

  2. Department of Mathematics, University of Oviedo, Oviedo, Spain

    Jesús S. Pérez del Río

  3. Department of Mathematics, University of Oviedo, Oviedo, Spain

    Antonio Pumariño

  4. Department of Mathematics, University of Oviedo, Oviedo, Spain

    J. Ángel Rodríguez

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Gasull, A., Giacomini, H. (2013). Some Applications of the Extended Bendixson-Dulac Theorem. In: Ibáñez, S., Pérez del Río, J., Pumariño, A., Rodríguez, J. (eds) Progress and Challenges in Dynamical Systems. Springer Proceedings in Mathematics & Statistics, vol 54. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38830-9_14

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