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

 

Existence theory for first order discontinuous functional differential equations


Authors: Eduardo Liz and Rodrigo L. Pouso
Journal: Proc. Amer. Math. Soc. 130 (2002), 3301-3311
MSC (1991): Primary 34A12, 34K07, 34K10
Published electronically: March 25, 2002
Corrigendum: Proc. Amer. Math. Soc. 132 (2004), 3135-3136.
MathSciNet review: 1913010
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Abstract: We prove the existence of extremal solutions for a first order functional differential equation subject to nonlinear boundary conditions of functional type. Moreover, the functions that define our problem are allowed to be discontinuous. The proof of our main result is based on a generalized iterative technique.


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Additional Information

Eduardo Liz
Affiliation: Departamento de Matemática Aplicada, E.T.S.E. Telecomunicación, Universidade de Vigo, Campus Marcosende, 36280 Vigo, Spain
Email: eliz@dma.uvigo.es

Rodrigo L. Pouso
Affiliation: Departamento de Análise Matemática, Facultade de Matemáticas, Campus Sur, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
Email: rodrigolp@correo.usc.es

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06480-8
PII: S 0002-9939(02)06480-8
Keywords: Discontinuous functional differential equations, extremal solutions, existence results
Received by editor(s): July 10, 2000
Received by editor(s) in revised form: June 13, 2001
Published electronically: March 25, 2002
Additional Notes: This research was partially supported by D.G.E.S. (Spain), projects PB97 – 0552 and HP1999-0026.
Communicated by: Carmen Chicone
Article copyright: © Copyright 2002 American Mathematical Society