Some Applications of the Extended Bendixson-Dulac Theorem

Armengol Gasull , Hector Giacomini (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

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.

Domaines: Analyse classique [math.CA]

Armengol Gasull, Hector Giacomini. Some Applications of the Extended Bendixson-Dulac Theorem. Santiago Ibáñez, Jesús S. Pérez del Río, Antonio Pumariño, J. Ángel Rodríguez. Progress and Challenges in Dynamical Systems, Springer, pp.233-252, 2013, Springer Proceedings in Mathematics & Statistics, ISBN 978-3-642-38829-3. ⟨hal-00869467⟩