About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 406727, 5 pages
http://dx.doi.org/10.1155/2013/406727
Research Article

Positive Fixed Points for Semipositone Operators in Ordered Banach Spaces and Applications

School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China

Received 23 January 2013; Accepted 7 April 2013

Academic Editor: Kunquan Lan

Copyright © 2013 Zengqin Zhao and Xinsheng Du. 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 theory of semipositone integral equations and semipositone ordinary differential equations has been emerging as an important area of investigation in recent years, but the research on semipositone operators in abstract spaces is yet rare. By employing a well-known fixed point index theorem and combining it with a translation substitution, we study the existence of positive fixed points for a semipositone operator in ordered Banach space. Lastly, we apply the results to Hammerstein integral equations of polynomial type.