On the extensions of the Darboux theory of integrability
Giné, Jaume (Universitat de Lleida. Departament de Matemàtica)
Grau, Maite (Universitat de Lleida. Departament de Matemàtica)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2013
Abstract:	Recently some extensions of the classical Darboux integrability theory to autonomous and non-autonomous polynomial vector fields have been done. The classical Darboux integrability theory and its recent extensions are based on the existence of algebraic invariant hypersurfaces. However the algebraicity of the invariant hypersurfaces is not necessary and the unique necessary condition is the algebraicity of the cofactors associated to them. In this note it is established a more general extension of the classical Darboux integrability theory.
Grants:	Ministerio de Ciencia e Innovación MTM2011-22877 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-381 Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 316338 European Commission 318999
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Nonlinear differential equations ; Integrability problem ; First integral ; Invariant curves ; Exponential factors
Published in:	Nonlinearity, Vol. 26 Núm. 8 (2013) , p. 2221-2229, ISSN 1361-6544

DOI: 10.1088/0951-7715/26/8/2221

Postprint 12 p, 727.4 KB

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