On a family of polynomial differential equations having at most three limit cycles
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Zhao, Yulin (Sun Yat-sen University(China), Department of Mathematics)

Date:	2013
Abstract:	We prove the existence of at most three limit cycles for a family of planar polynomial differential equations. Moreover we show that this upper bound in sharp. The key point in our approach is that the differential equations of this family can be transformed into Abel differential equations.
Grants:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2005/SGR-550
Note:	Agraïments/Ajudes: The first author is partially supported by by grants MTM2005-06098-C02-1. The second author is partially supported by the Spanish grant SAB-2005-0029, NSF of China (No.10571184) and SRF for ROCS, SEM. The second author also wants to express his thanks to the Departament de Matemàtiques of the Universitat Autònoma de Barcelona for the hospitality and support during the period in which this paper was started.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycle ; Polynomial differential system ; Abel equation ; Riccati equation
Published in:	Houston Journal of Mathematics, Vol. 39 Núm. 1 (2013) , p. 191-203, ISSN 0362-1588

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