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


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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Correspondence to Juan J. Nieto.

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★ 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).

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Key Words

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

Mathematics Subject Classification

  • Primary: 47H10
  • 34B15