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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Differential equations with limit-periodic forcings


Authors: Ana I. Alonso, Rafael Obaya and Rafael Ortega
Journal: Proc. Amer. Math. Soc. 131 (2003), 851-857
MSC (2000): Primary 34C11; Secondary 35B15
Published electronically: July 25, 2002
MathSciNet review: 1937423
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Abstract: The present paper is concerned with scalar differential equations of first order which are limit periodic in the independent variable. Some tools provided by the theories of exponential dichotomies and periodic differential equations are applied to prove that, in a generic sense, the existence of a bounded solution implies the existence of a limit periodic solution.


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Additional Information

Ana I. Alonso
Affiliation: E.T.S.I.I. Departamento de Matemática Aplicada a la Ingeniería, Paseo del Cauce s/n, 47011 Universidad de Valladolid, Spain
Email: anaalo@wmatem.eis.uva.es

Rafael Obaya
Affiliation: E.T.S.I.I. Departamento de Matemática Aplicada a la Ingeniería, Paseo del Cauce s/n, 47011 Universidad de Valladolid, Spain
Email: rafoba@wmatem.eis.uva.es

Rafael Ortega
Affiliation: Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
Email: rortega@ugr.es

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06692-3
PII: S 0002-9939(02)06692-3
Keywords: Limit-periodic equation, hyperbolic solution, almost-automorphic solution
Received by editor(s): October 16, 2001
Published electronically: July 25, 2002
Additional Notes: The first and second authors were partially supported by C.I.C.Y.T. under project PB98-0359 and by Junta de Castilla y León and European community under project VA19/00B. The third author was partially supported by DGES PB98-1294 (Spain)
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2002 American Mathematical Society