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

Order volume 22, pages 223–239 (2005)Cite this 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.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782, Santiago de Compostela, Spain

    Juan J. Nieto & Rosana Rodríguez-López

Authors
  1. Juan J. Nieto
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  2. Rosana Rodríguez-López
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Corresponding author

Correspondence to Juan J. Nieto.

Additional information

★ Partially supported by Ministerio de Ciencia y Tecnología/ FEDER, project BFM2001-3884-C02-01; and by Xunta de Galicia/ FEDER, project PGIDIT02PXIC20703PN.

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Nieto, J.J., Rodríguez-López, R. Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations. Order 22, 223–239 (2005). https://doi.org/10.1007/s11083-005-9018-5

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  • DOI: https://doi.org/10.1007/s11083-005-9018-5

Key Words

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

Mathematics Subject Classification

  • Primary: 47H10
  • 34B15