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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 603703, 9 pages
http://dx.doi.org/10.1155/2013/603703
Research Article

The Method of Coupled Fixed Points and Coupled Quasisolutions When Working with ODE’s with Arguments of Bounded Variation

1Department of Mathematical Analysis, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
2Department of Specific Didactics, University of Burgos, 09001 Burgos, Spain

Received 14 May 2013; Revised 2 October 2013; Accepted 4 October 2013

Academic Editor: Marcia Federson

Copyright © 2013 Rubén Figueroa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The aim of this paper is to show the use of the coupled quasisolutions method as a useful technique when dealing with ordinary differential equations with functional arguments of bounded variation. We will do this by looking for solutions for a first-order ordinary differential equation with an advanced argument of bounded variation. The main trick is to use the Jordan decomposition of this argument in a nondecreasing part and a nonincreasing one. As a necessary step, we will also talk about coupled fixed points of multivalued operators.