Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations
Acta Mathematica Sinica, English Series
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Acta Mathematica Sinica, English Series  2007, Vol. 23 Issue (12): 2205-2212    DOI: 10.1007/s10114-005-0769-0
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Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations
Juan J. NIETO, Rosana RODRÍGUEZ-LóPEZ
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.
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Juan J. NIETO
Rosana RODRÍGUEZ-LóPEZ
Key wordsfixed point   partially ordered set   first-order differential equation   lower and upper solutions     
Received: 2005-06-08;
Fund: Research partially supported by Ministerio de Educacióny Ciencia and FEDER,Project MTM2004-06652-C03-01,and by Xunta de Galicia and FEDER,Projects PGIDIT02PXIC20703PN and PGIDIT05PXIC20702PN
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Juan J. NIETO,Rosana RODRÍGUEZ-LóPEZ. Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations[J]. Acta Mathematica Sinica, English Series, 2007, 23(12): 2205-2212.
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http://www.actamath.com/Jwk_sxxb_en//EN/10.1007/s10114-005-0769-0      or     http://www.actamath.com/Jwk_sxxb_en//EN/Y2007/V23/I12/2205
 
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