Some applications of the extended Bendixson-Dulac theorem

Publicació amb motiu de Proceedings of the International Conference Dynamical Systems: 100 Years after Poincaré (September 2012, Gijón, Spain) amb el títol Progress and Challenges in Dynamical SystemsDuring 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