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

DOI:
https://doi.org/10.1090/S0002-9939-02-06692-3

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:
https://doi.org/10.1090/S0002-9939-02-06692-3

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