| Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations |
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| 摘 要： |
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| 关 键 词： | 常微分方程 固定点 半序集 上下解 |
| 收稿时间： | 8 June 2005 |
| 修稿时间： | 28 July 2005 |
Existence and Uniqueness of Fixed Point in Partially Ordered Sets
and Applications to Ordinary Differential Equations |
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| Authors: | Juan J Nieto Rosana Rodríguez-López |
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| Institution: | (1) Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782, Spain |
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| Abstract: | We prove some fixed point theorems in partially ordered sets, providing an extension of the
Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider
in this paper nonincreasing mappings as well as non monotone mappings. We also present some
applications to first–order ordinary differential equations with periodic boundary conditions, proving
the existence of a unique solution admitting the existence of a lower solution.
Research partially supported by Ministerio de Educación y Ciencia and FEDER, Project MTM2004-06652-C03-01, and by Xunta de
Galicia and FEDER, Projects PGIDIT02PXIC20703PN and PGIDIT05PXIC20702PN |
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| Keywords: | fixed point partially ordered set first-order differential equation lower and upper solutions |
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