ORIGINAL ARTICLES

Acta Mathematica Sinica, English Series

, Volume 23, Issue 12, pp 2205-2212

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

  • Juan J. NietoAffiliated withDepartamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Email author 
  • , Rosana Rodríguez-LópezAffiliated withDepartamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Email author 

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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.

Keywords

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

MR (2000) Subject Classification

47H10 34B15