On the number of polynomial solutions of Bernoulli and Abel polynomial differential equations
Cimà, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mañosas Capellades, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2017
Abstract:	In this paper we determine the maximum number of polynomial solutions of Bernoulli differential equations and of some integrable polynomial Abel differential equations. As far as we know, the tools used to prove our results have not been utilized before for studying this type of questions. We show that the addressed problems can be reduced to know the number of polynomial solutions of a related polynomial equation of arbitrary degree. Then we approach to these equations either applying several tools developed to study extended Fermat problems for polynomial equations, or reducing the question to the computation of the genus of some associated planar algebraic curves.
Grants:	Ministerio de Economía y Competitividad MTM2014-52209-C2-1-P Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014-SGR-555 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014-SGR-568
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Abel equation ; Bernouilli equation ; Generalized Fermat theorem for polynomials ; Genus of planar algebraic curves ; Polynomial solution ; Rational solution ; Ricatti equation
Published in:	Journal of differential equations, Vol. 263 (2017) , p. 7099-7122, ISSN 1090-2732

DOI: 10.1016/j.jde.2017.08.003

Postprint 24 p, 357.3 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
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