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, Volume 22, Issue 3, pp 223–239 | Cite as

Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations

  • Juan J. Nieto
  • Rosana Rodríguez-López
Article

Abstract

We prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions admitting only the existence of a lower solution. To this aim, we prove an appropriate fixed point theorem in partially ordered sets.

Key Words

fixed point partially ordered set first-order differential equation lower and upper solutions 

Mathematics Subject Classification

Primary: 47H10 34B15 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Departamento de Análisis Matemático, Facultad de MatemáticasUniversidad de Santiago de CompostelaSantiago de CompostelaSpain

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