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Periodic solutions of singular systems without the strong force condition


Authors: Daniel Franco and Pedro J. Torres
Journal: Proc. Amer. Math. Soc. 136 (2008), 1229-1236
MSC (2000): Primary 37J45, 34C25, 34B16.
DOI: https://doi.org/10.1090/S0002-9939-07-09226-X
Published electronically: December 27, 2007
MathSciNet review: 2367097
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Abstract: We present sufficient conditions for the existence of at least a non-collision periodic solution for singular systems under weak force conditions. We deal with two different types of systems. First, we assume that the system is generated by a potential, and then we consider systems without such hypothesis. In both cases we use the same technique based on Schauder fixed point theorem. Recent results in the literature are significantly improved.


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Additional Information

Daniel Franco
Affiliation: Departamento de Matemática Aplicada, UNED, ETSI Industriales, c/ Juan del Rosal 12, 28040 Madrid, Spain
Email: dfranco@ind.uned.es

Pedro J. Torres
Affiliation: Universidad de Granada, Departamento de Matemática Aplicada, 18071 Granada, Spain
Email: ptorres@ugr.es

DOI: https://doi.org/10.1090/S0002-9939-07-09226-X
Received by editor(s): August 17, 2006
Published electronically: December 27, 2007
Additional Notes: The first author was supported by D.G.I. MTM2004-06652-C03-03, Ministerio de Educación y Ciencia, Spain.
The second author was supported by D.G.I. MTM2005-03483, Ministerio de Educación y Ciencia, Spain.
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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