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Abstract and Applied Analysis
Volume 2014, Article ID 309613, 6 pages
http://dx.doi.org/10.1155/2014/309613
Research Article

Some Notes on the Existence of Solution for Ordinary Differential Equations via Fixed Point Theory

School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

Received 27 June 2014; Accepted 25 July 2014; Published 14 October 2014

Academic Editor: Wei-Shih Du

Copyright © 2014 Fei He. 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

We establish a fixed point theorem with w-distance for nonlinear contractive mappings in complete metric spaces. As applications of our results, we derive the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions. Here, we need not assume that the equation has a lower solution.