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

Authors

    • Departamento de Análisis MatemáticoFacultad de Matemáticas, Universidad de Santiago de Compostela, 15782
    • Departamento de Análisis MatemáticoFacultad de Matemáticas, Universidad de Santiago de Compostela, 15782
ORIGINAL ARTICLES

DOI: 10.1007/s10114-005-0769-0

Cite this article as:
Nieto, J.J. & Rodríguez-López, R. Acta. Math. Sin.-English Ser. (2007) 23: 2205. doi:10.1007/s10114-005-0769-0

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 pointpartially ordered setfirst–order differential equationlower and upper solutions

MR (2000) Subject Classification

47H1034B15

Copyright information

© Springer-Verlag Berlin Heidelberg 2006