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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the global solvability for overdetermined systems


Authors: Adalberto P. Bergamasco, Alexandre Kirilov, Wagner Vieira Leite Nunes and Sérgio Luís Zani
Journal: Trans. Amer. Math. Soc. 364 (2012), 4533-4549
MSC (2010): Primary 35A01, 35N10, 58J10
Published electronically: March 21, 2012
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Abstract: We consider a class of systems of two smooth vector fields on the 3-torus associated to a closed 1-form. We prove that the global solvability is completely determined by the connectedness of the sublevel and superlevel sets of a primitive of this 1-form in the minimal covering.


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Additional Information

Adalberto P. Bergamasco
Affiliation: Departamento de Matemática, ICMC-USP, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil
Email: apbergam@icmc.usp.br

Alexandre Kirilov
Affiliation: Departamento de Matemática, UFPR, Caixa Postal 19081, Curitiba, PR, 81531-990, Brazil
Email: akirilov@ufpr.br

Wagner Vieira Leite Nunes
Affiliation: Departamento de Matemática, ICMC-USP, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil
Email: wvlnunes@icmc.usp.br

Sérgio Luís Zani
Affiliation: Departamento de Matemática, ICMC-USP, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil
Email: szani@icmc.usp.br

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05414-6
PII: S 0002-9947(2012)05414-6
Keywords: Global solvability, connected sublevels and superlevels, minimal covering, commensurable periods, periodic solutions
Received by editor(s): January 14, 2010
Received by editor(s) in revised form: July 8, 2010
Published electronically: March 21, 2012
Additional Notes: The first and the fourth authors were partially supported by CNPq and FAPESP; the second author was partially supported by CNPq; the third author was partially supported by FAPESP
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.