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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★ 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
- fixed point
- partially ordered set
- first-order differential equation
- lower and upper solutions
Mathematics Subject Classification
- Primary: 47H10