Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations

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 fi...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2007-12, Vol.23 (12), p.2205-2212
Main Authors: Nieto, Juan J., Rodríguez-López, Rosana
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Differential equations
Hypotheses
Mapping
Mathematical analysis
Ordinary differential equations
Studies
Theorems
Uniqueness
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Summary: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.[PUBLICATION ABSTRACT]
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-005-0769-0